LMFDB - Embedded newform 230.2.l.a.157.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			157.7
Character	$\chi$	$=$	230.157
Dual form			230.2.l.a.63.7

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.349464 - 0.936950i) q^{2} +(-1.32977 + 2.43530i) q^{3} +(-0.755750 - 0.654861i) q^{4} +(-1.66077 - 1.49727i) q^{5} +(1.81704 + 2.09698i) q^{6} +(-2.11861 - 1.58597i) q^{7} +(-0.877679 + 0.479249i) q^{8} +(-2.54045 - 3.95301i) q^{9} +(-1.98325 + 1.03282i) q^{10} +(1.25057 + 0.571117i) q^{11} +(2.59975 - 0.969658i) q^{12} +(-3.57060 - 4.76976i) q^{13} +(-2.22635 + 1.43079i) q^{14} +(5.85475 - 2.05344i) q^{15} +(0.142315 + 0.989821i) q^{16} +(-1.72547 - 0.123408i) q^{17} +(-4.59157 + 0.998835i) q^{18} +(-2.57738 + 2.97445i) q^{19} +(0.274623 + 2.21914i) q^{20} +(6.67957 - 3.05046i) q^{21} +(0.972139 - 0.972139i) q^{22} +(-4.10342 - 2.48233i) q^{23} -2.77470i q^{24} +(0.516341 + 4.97327i) q^{25} +(-5.71682 + 1.67861i) q^{26} +(4.70208 - 0.336299i) q^{27} +(0.562548 + 2.58599i) q^{28} +(0.566767 - 0.491106i) q^{29} +(0.122055 - 6.20322i) q^{30} +(8.10734 + 2.38053i) q^{31} +(0.977147 + 0.212565i) q^{32} +(-3.05382 + 2.28606i) q^{33} +(-0.718617 + 1.57355i) q^{34} +(1.14390 + 5.80608i) q^{35} +(-0.668731 + 4.65113i) q^{36} +(-1.27823 + 5.87592i) q^{37} +(1.88621 + 3.45434i) q^{38} +(16.3639 - 2.35277i) q^{39} +(2.17519 + 0.518202i) q^{40} +(-7.72122 - 4.96213i) q^{41} +(-0.523855 - 7.32445i) q^{42} +(9.52665 + 5.20194i) q^{43} +(-0.571117 - 1.25057i) q^{44} +(-1.69963 + 10.3688i) q^{45} +(-3.75982 + 2.97721i) q^{46} +(-2.78897 - 2.78897i) q^{47} +(-2.59975 - 0.969658i) q^{48} +(0.00107183 + 0.00365032i) q^{49} +(4.84014 + 1.25419i) q^{50} +(2.59502 - 4.03793i) q^{51} +(-0.425051 + 5.94299i) q^{52} +(0.821926 - 1.09796i) q^{53} +(1.32811 - 4.52314i) q^{54} +(-1.22180 - 2.82095i) q^{55} +(2.61953 + 0.376632i) q^{56} +(-3.81634 - 10.2320i) q^{57} +(-0.262077 - 0.702656i) q^{58} +(-8.33749 - 1.19875i) q^{59} +(-5.76945 - 2.28216i) q^{60} +(0.141177 - 0.480803i) q^{61} +(5.06366 - 6.76426i) q^{62} +(-0.887149 + 12.4040i) q^{63} +(0.540641 - 0.841254i) q^{64} +(-1.21168 + 13.2677i) q^{65} +(1.07472 + 3.66017i) q^{66} +(3.10707 + 1.15888i) q^{67} +(1.22321 + 1.22321i) q^{68} +(11.5018 - 6.69210i) q^{69} +(5.83975 + 0.957241i) q^{70} +(-5.61249 - 12.2896i) q^{71} +(4.12417 + 2.25197i) q^{72} +(-1.04366 - 14.5923i) q^{73} +(5.05875 + 3.25106i) q^{74} +(-12.7980 - 5.35587i) q^{75} +(3.89570 - 0.560117i) q^{76} +(-1.74370 - 3.19335i) q^{77} +(3.51416 - 16.1543i) q^{78} +(0.692476 - 4.81627i) q^{79} +(1.24568 - 1.85695i) q^{80} +(0.422345 - 0.924807i) q^{81} +(-7.34755 + 5.50031i) q^{82} +(-0.232287 - 0.0505310i) q^{83} +(-7.04571 - 2.06881i) q^{84} +(2.68084 + 2.78846i) q^{85} +(8.20318 - 7.10810i) q^{86} +(0.442318 + 2.03330i) q^{87} +(-1.37131 + 0.0980779i) q^{88} +(11.7514 - 3.45054i) q^{89} +(9.12109 + 5.21600i) q^{90} +15.7681i q^{91} +(1.47558 + 4.56319i) q^{92} +(-16.5782 + 16.5782i) q^{93} +(-3.58776 + 1.63848i) q^{94} +(8.73401 - 1.08085i) q^{95} +(-1.81704 + 2.09698i) q^{96} +(-6.07227 + 1.32094i) q^{97} +(0.00379474 + 0.000271405i) q^{98} +(-0.919379 - 6.39442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{15}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.349464	−	0.936950i	0.247108	−	0.662524i
$2$	0.349464	−	0.936950i	0.247108	−	0.662524i
$3$	−1.32977	+	2.43530i	−0.767744	+	1.40602i	0.141579	+	0.989927i	$0.454782\pi$
$3$	−1.32977	+	2.43530i	−0.767744	+	1.40602i	−0.909323	+	0.416091i	$0.863400\pi$
$4$	−0.755750	−	0.654861i	−0.377875	−	0.327430i
$5$	−1.66077	−	1.49727i	−0.742721	−	0.669601i
$5$	−1.66077	−	1.49727i	−0.742721	−	0.669601i
$6$	1.81704	+	2.09698i	0.741804	+	0.856088i
$7$	−2.11861	−	1.58597i	−0.800759	−	0.599440i	0.118563	−	0.992946i	$-0.462171\pi$
$7$	−2.11861	−	1.58597i	−0.800759	−	0.599440i	−0.919322	+	0.393506i	$0.871262\pi$
$8$	−0.877679	+	0.479249i	−0.310306	+	0.169440i
$9$	−2.54045	−	3.95301i	−0.846816	−	1.31767i
$10$	−1.98325	+	1.03282i	−0.627159	+	0.326606i
$11$	1.25057	+	0.571117i	0.377062	+	0.172198i	0.594926	−	0.803781i	$-0.297182\pi$
$11$	1.25057	+	0.571117i	0.377062	+	0.172198i	−0.217864	+	0.975979i	$0.569909\pi$
$12$	2.59975	−	0.969658i	0.750484	−	0.279916i
$13$	−3.57060	−	4.76976i	−0.990306	−	1.32289i	−0.946101	−	0.323872i	$-0.895015\pi$
$13$	−3.57060	−	4.76976i	−0.990306	−	1.32289i	−0.0442052	−	0.999022i	$-0.514076\pi$
$14$	−2.22635	+	1.43079i	−0.595018	+	0.382395i
$15$	5.85475	−	2.05344i	1.51169	−	0.530197i
$16$	0.142315	+	0.989821i	0.0355787	+	0.247455i
$17$	−1.72547	−	0.123408i	−0.418488	−	0.0299309i	−0.139492	−	0.990223i	$-0.544547\pi$
$17$	−1.72547	−	0.123408i	−0.418488	−	0.0299309i	−0.278996	+	0.960292i	$0.590002\pi$
$18$	−4.59157	+	0.998835i	−1.08224	+	0.235428i
$19$	−2.57738	+	2.97445i	−0.591291	+	0.682386i	−0.969993	−	0.243133i	$-0.921825\pi$
$19$	−2.57738	+	2.97445i	−0.591291	+	0.682386i	0.378702	+	0.925519i	$0.376370\pi$
$20$	0.274623	+	2.21914i	0.0614077	+	0.496215i
$21$	6.67957	−	3.05046i	1.45760	−	0.665665i
$22$	0.972139	−	0.972139i	0.207261	−	0.207261i
$23$	−4.10342	−	2.48233i	−0.855622	−	0.517601i
$23$	−4.10342	−	2.48233i	−0.855622	−	0.517601i
$24$		−	2.77470i		−	0.566383i
$25$	0.516341	+	4.97327i	0.103268	+	0.994654i
$26$	−5.71682	+	1.67861i	−1.12116	+	0.329203i
$27$	4.70208	−	0.336299i	0.904916	−	0.0647209i
$28$	0.562548	+	2.58599i	0.106312	+	0.488706i
$29$	0.566767	−	0.491106i	0.105246	−	0.0911961i	−0.600648	−	0.799513i	$-0.705091\pi$
$29$	0.566767	−	0.491106i	0.105246	−	0.0911961i	0.705894	+	0.708317i	$0.250545\pi$
$30$	0.122055	−	6.20322i	0.0222840	−	1.13255i
$31$	8.10734	+	2.38053i	1.45612	+	0.427556i	0.911561	−	0.411165i	$-0.134878\pi$
$31$	8.10734	+	2.38053i	1.45612	+	0.427556i	0.544561	+	0.838721i	$0.316696\pi$
$32$	0.977147	+	0.212565i	0.172737	+	0.0375766i
$33$	−3.05382	+	2.28606i	−0.531601	+	0.397952i
$34$	−0.718617	+	1.57355i	−0.123242	+	0.269862i
$35$	1.14390	+	5.80608i	0.193354	+	0.981406i
$36$	−0.668731	+	4.65113i	−0.111455	+	0.775188i
$37$	−1.27823	+	5.87592i	−0.210139	+	0.965995i	0.744359	+	0.667779i	$0.232755\pi$
$37$	−1.27823	+	5.87592i	−0.210139	+	0.965995i	−0.954499	+	0.298216i	$0.903609\pi$
$38$	1.88621	+	3.45434i	0.305984	+	0.560367i
$39$	16.3639	−	2.35277i	2.62032	−	0.376744i
$40$	2.17519	+	0.518202i	0.343928	+	0.0819349i
$41$	−7.72122	−	4.96213i	−1.20585	−	0.774954i	−0.225892	−	0.974152i	$-0.572530\pi$
$41$	−7.72122	−	4.96213i	−1.20585	−	0.774954i	−0.979959	+	0.199199i	$0.936166\pi$
$42$	−0.523855	−	7.32445i	−0.0808326	−	1.13019i
$43$	9.52665	+	5.20194i	1.45280	+	0.793289i	0.995385	−	0.0959639i	$-0.0305933\pi$
$43$	9.52665	+	5.20194i	1.45280	+	0.793289i	0.457416	+	0.889253i	$0.348775\pi$
$44$	−0.571117	−	1.25057i	−0.0860992	−	0.188531i
$45$	−1.69963	+	10.3688i	−0.253367	+	1.54569i
$46$	−3.75982	+	2.97721i	−0.554355	+	0.438966i
$47$	−2.78897	−	2.78897i	−0.406813	−	0.406813i	0.473813	−	0.880625i	$-0.342877\pi$
$47$	−2.78897	−	2.78897i	−0.406813	−	0.406813i	−0.880625	+	0.473813i	$0.842877\pi$
$48$	−2.59975	−	0.969658i	−0.375242	−	0.139958i
$49$	0.00107183	+	0.00365032i	0.000153119	+	0.000521475i
$50$	4.84014	+	1.25419i	0.684500	+	0.177370i
$51$	2.59502	−	4.03793i	0.363375	−	0.565423i
$52$	−0.425051	+	5.94299i	−0.0589440	+	0.824145i
$53$	0.821926	−	1.09796i	0.112900	−	0.150817i	−0.740532	−	0.672022i	$-0.765426\pi$
$53$	0.821926	−	1.09796i	0.112900	−	0.150817i	0.853432	+	0.521205i	$0.174517\pi$
$54$	1.32811	−	4.52314i	0.180733	−	0.615521i
$55$	−1.22180	−	2.82095i	−0.164747	−	0.380376i
$56$	2.61953	+	0.376632i	0.350050	+	0.0503296i
$57$	−3.81634	−	10.2320i	−0.505487	−	1.35526i
$58$	−0.262077	−	0.702656i	−0.0344124	−	0.0922633i
$59$	−8.33749	−	1.19875i	−1.08545	−	0.156064i	−0.423710	−	0.905798i	$-0.639272\pi$
$59$	−8.33749	−	1.19875i	−1.08545	−	0.156064i	−0.661739	+	0.749734i	$0.730181\pi$
$60$	−5.76945	−	2.28216i	−0.744832	−	0.294626i
$61$	0.141177	−	0.480803i	0.0180758	−	0.0615606i	−0.949961	−	0.312368i	$-0.898878\pi$
$61$	0.141177	−	0.480803i	0.0180758	−	0.0615606i	0.968037	+	0.250807i	$0.0806960\pi$
$62$	5.06366	−	6.76426i	0.643086	−	0.859062i
$63$	−0.887149	+	12.4040i	−0.111770	+	1.56275i
$64$	0.540641	−	0.841254i	0.0675801	−	0.105157i
$65$	−1.21168	+	13.2677i	−0.150291	+	1.64565i
$66$	1.07472	+	3.66017i	0.132289	+	0.450535i
$67$	3.10707	+	1.15888i	0.379589	+	0.141579i	0.532014	−	0.846736i	$-0.321435\pi$
$67$	3.10707	+	1.15888i	0.379589	+	0.141579i	−0.152425	+	0.988315i	$0.548708\pi$
$68$	1.22321	+	1.22321i	0.148336	+	0.148336i
$69$	11.5018	−	6.69210i	1.38466	−	0.805635i
$70$	5.83975	+	0.957241i	0.697984	+	0.114412i
$71$	−5.61249	−	12.2896i	−0.666080	−	1.45851i	−0.876746	−	0.480953i	$-0.840291\pi$
$71$	−5.61249	−	12.2896i	−0.666080	−	1.45851i	0.210667	−	0.977558i	$-0.432436\pi$
$72$	4.12417	+	2.25197i	0.486039	+	0.265397i
$73$	−1.04366	−	14.5923i	−0.122151	−	1.70789i	−0.576522	−	0.817081i	$-0.695591\pi$
$73$	−1.04366	−	14.5923i	−0.122151	−	1.70789i	0.454371	−	0.890812i	$-0.349864\pi$
$74$	5.05875	+	3.25106i	0.588067	+	0.377928i
$75$	−12.7980	−	5.35587i	−1.47778	−	0.618442i
$76$	3.89570	−	0.560117i	0.446868	−	0.0642499i
$77$	−1.74370	−	3.19335i	−0.198713	−	0.363916i
$78$	3.51416	−	16.1543i	0.397900	−	1.82912i
$79$	0.692476	−	4.81627i	0.0779096	−	0.541873i	−0.913064	−	0.407816i	$-0.866290\pi$
$79$	0.692476	−	4.81627i	0.0779096	−	0.541873i	0.990974	−	0.134057i	$-0.0428005\pi$
$80$	1.24568	−	1.85695i	0.139271	−	0.207614i
$81$	0.422345	−	0.924807i	0.0469272	−	0.102756i
$82$	−7.34755	+	5.50031i	−0.811401	+	0.607407i
$83$	−0.232287	−	0.0505310i	−0.0254968	−	0.00554650i	0.199799	−	0.979837i	$-0.435971\pi$
$83$	−0.232287	−	0.0505310i	−0.0254968	−	0.00554650i	−0.225296	+	0.974290i	$0.572335\pi$
$84$	−7.04571	−	2.06881i	−0.768750	−	0.225725i
$85$	2.68084	+	2.78846i	0.290778	+	0.302450i
$86$	8.20318	−	7.10810i	0.884572	−	0.766486i
$87$	0.442318	+	2.03330i	0.0474215	+	0.217993i
$88$	−1.37131	+	0.0980779i	−0.146182	+	0.0104551i
$89$	11.7514	−	3.45054i	1.24565	−	0.365756i	0.408515	−	0.912752i	$-0.366047\pi$
$89$	11.7514	−	3.45054i	1.24565	−	0.365756i	0.837136	+	0.546995i	$0.184229\pi$
$90$	9.12109	+	5.21600i	0.961447	+	0.549815i
$91$			15.7681i			1.65295i
$92$	1.47558	+	4.56319i	0.153839	+	0.475745i
$93$	−16.5782	+	16.5782i	−1.71908	+	1.71908i
$94$	−3.58776	+	1.63848i	−0.370050	+	0.168996i
$95$	8.73401	−	1.08085i	0.896090	−	0.110893i
$96$	−1.81704	+	2.09698i	−0.185451	+	0.214022i
$97$	−6.07227	+	1.32094i	−0.616546	+	0.134121i	−0.509983	−	0.860185i	$-0.670348\pi$
$97$	−6.07227	+	1.32094i	−0.616546	+	0.134121i	−0.106563	+	0.994306i	$0.533985\pi$
$98$	0.00379474		0.000271405i	0.000383326		2.74160e-5i
$99$	−0.919379	−	6.39442i	−0.0924011	−	0.642664i
$100$	2.86657	−	4.09668i	0.286657	−	0.409668i
$101$	−10.1269	+	6.50814i	−1.00766	+	0.647584i	−0.936787	−	0.349901i	$-0.886215\pi$
$101$	−10.1269	+	6.50814i	−1.00766	+	0.647584i	−0.0708740	+	0.997485i	$0.522579\pi$
$102$	−2.87647	−	3.84251i	−0.284813	−	0.380465i
$103$	−2.81288	+	1.04915i	−0.277162	+	0.103376i	−0.484201	−	0.874957i	$-0.660890\pi$
$103$	−2.81288	+	1.04915i	−0.277162	+	0.103376i	0.207040	+	0.978333i	$0.433617\pi$
$104$	5.41974	+	2.47511i	0.531450	+	0.242705i
$105$	−15.6606	−	4.93503i	−1.52832	−	0.481609i
$106$	−0.741504	−	1.15380i	−0.0720212	−	0.112067i
$107$	−12.1888	+	6.65557i	−1.17833	+	0.643418i	−0.944388	−	0.328832i	$-0.893345\pi$
$107$	−12.1888	+	6.65557i	−1.17833	+	0.643418i	−0.233944	+	0.972250i	$0.575163\pi$
$108$	−3.77382	−	2.82505i	−0.363136	−	0.271841i
$109$	6.76218	+	7.80397i	0.647699	+	0.747484i	0.980716	−	0.195436i	$-0.0626123\pi$
$109$	6.76218	+	7.80397i	0.647699	+	0.747484i	−0.333017	+	0.942921i	$0.608067\pi$
$110$	−3.07006	+	0.158945i	−0.292719	+	0.0151548i
$111$	−12.6098	−	10.9265i	−1.19687	−	1.03710i
$112$	1.26832	−	2.32275i	0.119845	−	0.219479i
$113$	−4.87945	+	13.0823i	−0.459020	+	1.23068i	0.477053	+	0.878875i	$0.341705\pi$
$113$	−4.87945	+	13.0823i	−0.459020	+	1.23068i	−0.936073	+	0.351806i	$0.885568\pi$
$114$	−10.9206			−1.02280
$115$	3.09812	+	10.2665i	0.288902	+	0.957359i
$116$	−0.749940			−0.0696302
$117$	−9.78402	+	26.2320i	−0.904533	+	2.42515i
$118$	−4.03683	+	7.39289i	−0.371620	+	0.680571i
$119$	3.45988	+	2.99800i	0.317166	+	0.274826i
$120$	−4.15448	+	4.60815i	−0.379251	+	0.420664i
$121$	−5.96571	−	6.88480i	−0.542337	−	0.625891i
$122$	−0.401152	−	0.300299i	−0.0363186	−	0.0271878i
$123$	22.3517	−	12.2049i	2.01538	−	1.10048i
$124$	−4.56821	−	7.10827i	−0.410237	−	0.638341i
$125$	6.58882	−	9.03258i	0.589322	−	0.807898i
$126$	11.3119	+	5.16595i	1.00774	+	0.460220i
$127$	14.7037	−	5.48421i	1.30474	−	0.486645i	0.401535	−	0.915844i	$-0.368477\pi$
$127$	14.7037	−	5.48421i	1.30474	−	0.486645i	0.903210	+	0.429199i	$0.141204\pi$
$128$	−0.599278	−	0.800541i	−0.0529692	−	0.0707585i
$129$	−25.3365	+	16.2828i	−2.23076	+	1.43362i
$130$	12.0077	+	5.77186i	1.05314	+	0.506226i
$131$	−0.695018	−	4.83395i	−0.0607240	−	0.422345i	−0.997395	−	0.0721340i	$-0.977019\pi$
$131$	−0.695018	−	4.83395i	−0.0607240	−	0.422345i	0.936671	−	0.350211i	$-0.113890\pi$
$132$	3.80497	+	0.272137i	0.331180	+	0.0236865i
$133$	10.1778	−	2.21405i	0.882531	−	0.191983i
$134$	2.17162	−	2.50618i	0.187599	−	0.216501i
$135$	−8.31263	−	6.48178i	−0.715437	−	0.557863i
$136$	1.57355	−	0.718617i	0.134931	−	0.0616209i
$137$	5.35840	−	5.35840i	0.457799	−	0.457799i	−0.440134	−	0.897932i	$-0.645069\pi$
$137$	5.35840	−	5.35840i	0.457799	−	0.457799i	0.897932	+	0.440134i	$0.145069\pi$
$138$	−2.25069	−	13.1153i	−0.191592	−	1.11645i
$139$			15.1640i			1.28620i	0.765783	+	0.643099i	$0.222352\pi$
$139$			15.1640i			1.28620i	−0.765783	+	0.643099i	$0.777648\pi$
$140$	2.93767	−	5.13703i	0.248279	−	0.434159i
$141$	10.5006	−	3.08327i	0.884314	−	0.259658i
$142$	−13.4761	+	0.963832i	−1.13089	+	0.0808830i
$143$	−1.74120	−	8.00417i	−0.145606	−	0.669342i
$144$	3.55123	−	3.07716i	0.295936	−	0.256430i
$145$	−1.67659	−	0.0329886i	−0.139233	−	0.00273956i
$146$	−14.0369	−	4.12161i	−1.16170	−	0.341107i
$147$	−0.0103149	−	0.00224387i	−0.000850760	−	0.000185071i
$148$	4.81393	−	3.60366i	0.395702	−	0.296219i
$149$	6.54971	−	14.3419i	0.536573	−	1.17493i	−0.426202	−	0.904628i	$-0.640149\pi$
$149$	6.54971	−	14.3419i	0.536573	−	1.17493i	0.962775	−	0.270303i	$-0.0871239\pi$
$150$	−9.49062	+	10.1194i	−0.774906	+	0.826245i
$151$	0.405528	−	2.82051i	0.0330014	−	0.229530i	−0.966645	−	0.256120i	$-0.917556\pi$
$151$	0.405528	−	2.82051i	0.0330014	−	0.229530i	0.999646	+	0.0265900i	$0.00846487\pi$
$152$	0.836607	−	3.84582i	0.0678578	−	0.311937i
$153$	3.89563	+	7.13432i	0.314943	+	0.576776i
$154$	−3.60136	+	0.517798i	−0.290206	+	0.0417254i
$155$	−9.90016	−	16.0924i	−0.795200	−	1.29258i
$156$	−13.9077	−	8.93795i	−1.11351	−	0.715609i
$157$	−1.41981	−	19.8516i	−0.113313	−	1.58433i	−0.662781	−	0.748813i	$-0.730624\pi$
$157$	−1.41981	−	19.8516i	−0.113313	−	1.58433i	0.549468	−	0.835515i	$-0.314831\pi$
$158$	−4.27061	−	2.33193i	−0.339752	−	0.185518i
$159$	1.58089	+	3.46167i	0.125373	+	0.274529i
$160$	−1.30455	−	1.81608i	−0.103134	−	0.143574i
$161$	4.75664	+	11.7670i	0.374875	+	0.927368i
$162$	−0.718903	−	0.718903i	−0.0564823	−	0.0564823i
$163$	0.0590420	+	0.0220215i	0.00462452	+	0.00172486i	0.351775	−	0.936084i	$-0.385578\pi$
$163$	0.0590420	+	0.0220215i	0.00462452	+	0.00172486i	−0.347151	+	0.937809i	$0.612851\pi$
$164$	2.58581	+	8.80645i	0.201918	+	0.687668i
$165$	8.49455	+	0.775773i	0.661300	+	0.0603939i
$166$	−0.128521	+	0.199983i	−0.00997517	+	0.0155217i
$167$	−0.121267	+	1.69553i	−0.00938389	+	0.131204i	−0.999984	−	0.00558276i	$-0.998223\pi$
$167$	−0.121267	+	1.69553i	−0.00938389	+	0.131204i	0.990601	+	0.136787i	$0.0436775\pi$
$168$	−4.40059	+	5.87850i	−0.339513	+	0.453536i
$169$	−6.33893	+	21.5884i	−0.487610	+	1.66065i
$170$	3.54950	−	1.53735i	0.272234	−	0.117909i
$171$	18.3057	+	2.63197i	1.39987	+	0.201272i
$172$	−3.79321	−	10.1700i	−0.289230	−	0.775455i
$173$	−3.27587	−	8.78296i	−0.249060	−	0.667756i	−0.999973	−	0.00735456i	$-0.997659\pi$
$173$	−3.27587	−	8.78296i	−0.249060	−	0.667756i	0.750913	−	0.660401i	$-0.229614\pi$
$174$	2.05968	+	0.296137i	0.156144	+	0.0224501i
$175$	6.79353	−	11.3553i	0.513543	−	0.858381i
$176$	−0.387329	+	1.31912i	−0.0291960	+	0.0994326i
$177$	14.0063	−	18.7102i	1.05278	−	1.40634i
$178$	0.873731	−	12.2164i	0.0654889	−	0.915654i
$179$	1.20944	−	1.88192i	0.0903975	−	0.140661i	−0.793110	−	0.609079i	$-0.791539\pi$
$179$	1.20944	−	1.88192i	0.0903975	−	0.140661i	0.883507	+	0.468417i	$0.155176\pi$
$180$	8.07462	−	6.72320i	0.601847	−	0.501118i
$181$	3.49917	+	11.9171i	0.260091	+	0.885789i	0.981204	+	0.192972i	$0.0618126\pi$
$181$	3.49917	+	11.9171i	0.260091	+	0.885789i	−0.721113	+	0.692817i	$0.756369\pi$
$182$	14.7739	+	5.51040i	1.09512	+	0.408458i
$183$	0.983166	+	0.983166i	0.0726777	+	0.0726777i
$184$	4.79114	+	0.212129i	0.353207	+	0.0156384i
$185$	10.9207	−	7.84472i	0.802906	−	0.576755i
$186$	9.73946	+	21.3264i	0.714132	+	1.56373i
$187$	−2.08735	−	1.13978i	−0.152642	−	0.0833488i
$188$	0.281376	+	3.93414i	0.0205214	+	0.286927i
$189$	−10.4952	−	6.74487i	−0.763416	−	0.490617i
$190$	2.03952	−	8.56105i	0.147962	−	0.621084i
$191$	−12.0591	+	1.73384i	−0.872566	+	0.125456i	−0.564028	−	0.825756i	$-0.690749\pi$
$191$	−12.0591	+	1.73384i	−0.872566	+	0.125456i	−0.308538	+	0.951212i	$0.599840\pi$
$192$	1.32977	+	2.43530i	0.0959680	+	0.175752i
$193$	−0.703786	+	3.23525i	−0.0506596	+	0.232879i	−0.995514	−	0.0946114i	$-0.969839\pi$
$193$	−0.703786	+	3.23525i	−0.0506596	+	0.232879i	0.944855	+	0.327490i	$0.106203\pi$
$194$	−0.884385	+	6.15103i	−0.0634951	+	0.441618i
$195$	−30.6994	−	20.5938i	−2.19843	−	1.47475i
$196$	0.00158042	−	0.00346063i	0.000112887	−	0.000247188i
$197$	14.3204	−	10.7201i	1.02029	−	0.763779i	0.0483064	−	0.998833i	$-0.484618\pi$
$197$	14.3204	−	10.7201i	1.02029	−	0.763779i	0.971982	+	0.235054i	$0.0755267\pi$
$198$	−6.31254	−	1.37321i	−0.448613	−	0.0975898i
$199$	−21.3398	−	6.26592i	−1.51274	−	0.444179i	−0.583020	−	0.812458i	$-0.698129\pi$
$199$	−21.3398	−	6.26592i	−1.51274	−	0.444179i	−0.929715	+	0.368279i	$0.879947\pi$
$200$	−2.83662	−	4.11748i	−0.200579	−	0.291150i
$201$	−6.95390	+	6.02559i	−0.490491	+	0.425012i
$202$	2.55882	+	11.7627i	0.180038	+	0.827622i
$203$	−1.97964	+	0.141586i	−0.138943	+	0.00993742i
$204$	−4.60546	+	1.35229i	−0.322447	+	0.0946789i
$205$	5.39354	+	19.8017i	0.376701	+	1.38301i
$206$			3.00217i			0.209171i
$207$	0.611837	+	22.5271i	0.0425256	+	1.56574i
$208$	4.21306	−	4.21306i	0.292123	−	0.292123i
$209$	−4.92196	+	2.24778i	−0.340459	+	0.155482i
$210$	−10.0967	+	12.9486i	−0.696739	+	0.893539i
$211$	−5.39990	+	6.23182i	−0.371745	+	0.429016i	−0.910540	−	0.413420i	$-0.864334\pi$
$211$	−5.39990	+	6.23182i	−0.371745	+	0.429016i	0.538796	+	0.842436i	$0.318879\pi$
$212$	−1.34018	+	0.291539i	−0.0920442	+	0.0200230i
$213$	37.3922	+	2.67434i	2.56207	+	0.183243i
$214$	1.97640	+	13.7461i	0.135104	+	0.939667i
$215$	−8.03288	−	22.9033i	−0.547838	−	1.56199i
$216$	−3.96575	+	2.54863i	−0.269835	+	0.173412i
$217$	−13.4008	−	17.9014i	−0.909708	−	1.21523i
$218$	9.67506	−	3.60861i	0.655278	−	0.244406i
$219$	36.9243	+	16.8627i	2.49511	+	1.13948i
$220$	−0.923953	+	2.93204i	−0.0622929	+	0.197678i
$221$	5.57234	+	8.67073i	0.374836	+	0.583256i
$222$	−14.6443	+	7.99637i	−0.982859	+	0.536681i
$223$	12.7123	+	9.51627i	0.851276	+	0.637257i	0.933190	−	0.359382i	$-0.117013\pi$
$223$	12.7123	+	9.51627i	0.851276	+	0.637257i	−0.0819148	+	0.996639i	$0.526104\pi$
$224$	−1.73307	−	2.00007i	−0.115796	−	0.133635i
$225$	18.3477	−	14.6754i	1.22318	−	0.978362i
$226$	10.5523	+	9.14360i	0.701927	+	0.608223i
$227$	−10.6108	+	19.4321i	−0.704260	+	1.28976i	0.243229	+	0.969969i	$0.421793\pi$
$227$	−10.6108	+	19.4321i	−0.704260	+	1.28976i	−0.947489	+	0.319788i	$0.896388\pi$
$228$	−3.81634	+	10.2320i	−0.252744	+	0.677632i
$229$	−11.3129			−0.747578			−0.373789	−	0.927514i	$-0.621942\pi$
$229$	−11.3129			−0.747578			−0.373789	+	0.927514i	$0.621942\pi$
$230$	10.7019	+	0.684998i	0.705663	+	0.0451674i
$231$	10.0955			0.664233
$232$	−0.262077	+	0.702656i	−0.0172062	+	0.0461316i
$233$	2.31326	−	4.23642i	0.151547	−	0.277537i	−0.790866	−	0.611990i	$-0.790369\pi$
$233$	2.31326	−	4.23642i	0.151547	−	0.277537i	0.942413	+	0.334452i	$0.108551\pi$
$234$	21.1589	+	18.3343i	1.38320	+	1.19855i
$235$	0.455997	+	8.80769i	0.0297459	+	0.574550i
$236$	5.51604	+	6.36585i	0.359064	+	0.414382i
$237$	10.8082	+	8.09093i	0.702069	+	0.525562i
$238$	4.01808	−	2.19404i	0.260453	−	0.142218i
$239$	−4.00693	−	6.23490i	−0.259187	−	0.403302i	0.687134	−	0.726530i	$-0.258868\pi$
$239$	−4.00693	−	6.23490i	−0.259187	−	0.403302i	−0.946321	+	0.323228i	$0.895232\pi$
$240$	2.86576	+	5.50293i	0.184984	+	0.355212i
$241$	−5.82788	−	2.66150i	−0.375407	−	0.171442i	0.218771	−	0.975776i	$-0.429795\pi$
$241$	−5.82788	−	2.66150i	−0.375407	−	0.171442i	−0.594178	+	0.804334i	$0.702522\pi$
$242$	−8.53551	+	3.18358i	−0.548683	+	0.204648i
$243$	10.1657	+	13.5798i	0.652130	+	0.871144i
$244$	−0.421553	+	0.270916i	−0.0269872	+	0.0173436i
$245$	0.00368547	−	0.00766719i	0.000235456	−	0.000489839i
$246$	−3.62431	−	25.2076i	−0.231077	−	1.60718i
$247$	23.3902	+	1.67290i	1.48828	+	0.106444i
$248$	−8.25651	+	1.79609i	−0.524289	+	0.114052i
$249$	0.431947	−	0.498493i	0.0273735	−	0.0315907i
$250$	−6.16052	−	9.32995i	−0.389625	−	0.590078i
$251$	16.0945	−	7.35010i	1.01587	−	0.463934i	0.163320	−	0.986573i	$-0.447780\pi$
$251$	16.0945	−	7.35010i	1.01587	−	0.463934i	0.852554	+	0.522639i	$0.175052\pi$
$252$	8.79333	−	8.79333i	0.553928	−	0.553928i
$253$	−3.71392	−	5.44787i	−0.233492	−	0.342504i
$254$		−	15.6932i		−	0.984678i
$255$	−10.3556	+	2.82063i	−0.648494	+	0.176635i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	12.5247	−	0.895787i	0.781272	−	0.0558777i	0.324995	−	0.945716i	$-0.394637\pi$
$257$	12.5247	−	0.895787i	0.781272	−	0.0558777i	0.456277	+	0.889838i	$0.349183\pi$
$258$	6.40196	+	29.4293i	0.398568	+	1.83219i
$259$	12.0271	−	10.4215i	0.747327	−	0.647563i
$260$	9.60420	−	9.23355i	0.595627	−	0.572640i
$261$	−3.38119	−	0.992807i	−0.209290	−	0.0614532i
$262$	−4.77206	−	1.03810i	−0.294819	−	0.0641339i
$263$	−20.7811	+	15.5565i	−1.28142	+	0.959257i	−1.00000		0.000328105i	$-0.999896\pi$
$263$	−20.7811	+	15.5565i	−1.28142	+	0.959257i	−0.281418	+	0.959585i	$0.590805\pi$
$264$	1.58468	−	3.46996i	0.0975303	−	0.213561i
$265$	−3.00899	+	0.592823i	−0.184841	+	0.0364168i
$266$	1.48233	−	10.3099i	0.0908877	−	0.632138i
$267$	−7.22367	+	33.2067i	−0.442081	+	2.03221i
$268$	−1.58926	−	2.91052i	−0.0970798	−	0.177788i
$269$	−10.0983	+	1.45191i	−0.615702	+	0.0885245i	−0.443108	−	0.896468i	$-0.646124\pi$
$269$	−10.0983	+	1.45191i	−0.615702	+	0.0885245i	−0.172594	+	0.984993i	$0.555215\pi$
$270$	−8.97807	+	5.52336i	−0.546388	+	0.336141i
$271$	−2.21069	−	1.42072i	−0.134290	−	0.0863028i	0.471771	−	0.881721i	$-0.343615\pi$
$271$	−2.21069	−	1.42072i	−0.134290	−	0.0863028i	−0.606061	+	0.795418i	$0.707251\pi$
$272$	−0.123408	−	1.72547i	−0.00748271	−	0.104622i
$273$	−38.4000	−	20.9680i	−2.32408	−	1.26904i
$274$	−3.14798	−	6.89312i	−0.190176	−	0.416428i
$275$	−2.19460	+	6.51432i	−0.132339	+	0.392829i
$276$	−13.0749	−	2.47453i	−0.787016	−	0.148949i
$277$	−2.04506	−	2.04506i	−0.122876	−	0.122876i	0.642995	−	0.765871i	$-0.277692\pi$
$277$	−2.04506	−	2.04506i	−0.122876	−	0.122876i	−0.765871	+	0.642995i	$0.777692\pi$
$278$	14.2079	+	5.29929i	0.852136	+	0.317830i
$279$	−11.1860	−	38.0961i	−0.669689	−	2.28075i
$280$	−3.78653	−	4.54766i	−0.226289	−	0.271775i
$281$	11.0785	−	17.2385i	0.660890	−	1.02836i	−0.335381	−	0.942083i	$-0.608865\pi$
$281$	11.0785	−	17.2385i	0.660890	−	1.02836i	0.996271	−	0.0862818i	$-0.0274986\pi$
$282$	0.780733	−	10.9161i	0.0464919	−	0.650042i
$283$	−2.52827	+	3.37738i	−0.150290	+	0.200764i	−0.869368	−	0.494166i	$-0.835474\pi$
$283$	−2.52827	+	3.37738i	−0.150290	+	0.200764i	0.719078	+	0.694930i	$0.244565\pi$
$284$	−3.80636	+	12.9633i	−0.225866	+	0.769229i
$285$	−8.98204	+	22.7072i	−0.532050	+	1.34506i
$286$	−8.10799	−	1.16575i	−0.479435	−	0.0689324i
$287$	8.48845	+	22.7584i	0.501058	+	1.34339i
$288$	−1.64212	−	4.40269i	−0.0967627	−	0.259431i
$289$	−13.8649	−	1.99348i	−0.815585	−	0.117263i
$290$	−0.616818	+	1.55935i	−0.0362208	+	0.0915684i
$291$	4.85785	−	16.5443i	0.284772	−	0.969845i
$292$	−8.76715	+	11.7115i	−0.513059	+	0.685366i
$293$	0.532871	−	7.45052i	0.0311307	−	0.435264i	−0.957855	−	0.287252i	$-0.907258\pi$
$293$	0.532871	−	7.45052i	0.0311307	−	0.435264i	0.988986	−	0.148012i	$-0.0472873\pi$
$294$	−0.00570709	+	0.00888040i	−0.000332844	+	0.000517915i
$295$	12.0518	+	14.4744i	0.701685	+	0.842730i
$296$	−1.69415	−	5.76976i	−0.0984707	−	0.335360i
$297$	6.07236	+	2.26487i	0.352354	+	0.131421i
$298$	−11.1487	−	11.1487i	−0.645828	−	0.645828i
$299$	2.81154	+	28.4357i	0.162596	+	1.64448i
$300$	6.16473	+	12.4286i	0.355921	+	0.717565i
$301$	−11.9331	−	26.1299i	−0.687813	−	1.50610i
$302$	−2.50096	−	1.36563i	−0.143914	−	0.0785830i
$303$	−2.38282	−	33.3162i	−0.136890	−	1.91397i
$304$	−3.31097	−	2.12783i	−0.189897	−	0.122040i
$305$	−0.954357	+	0.587126i	−0.0546463	+	0.0336187i
$306$	8.04588	−	1.15682i	0.459953	−	0.0661312i
$307$	−10.2450	−	18.7623i	−0.584712	−	1.07082i	−0.987810	−	0.155663i	$-0.950248\pi$
$307$	−10.2450	−	18.7623i	−0.584712	−	1.07082i	0.403098	−	0.915157i	$-0.367933\pi$
$308$	−0.773397	+	3.55525i	−0.0440684	+	0.202579i
$309$	1.18550	−	8.24533i	0.0674407	−	0.469060i
$310$	−18.5376	+	3.65222i	−1.05286	+	0.207432i
$311$	−11.6819	+	25.5797i	−0.662418	+	1.45049i	0.217833	+	0.975986i	$0.430101\pi$
$311$	−11.6819	+	25.5797i	−0.662418	+	1.45049i	−0.880251	+	0.474508i	$0.842626\pi$
$312$	−13.2347	+	9.90734i	−0.749265	+	0.560893i
$313$	19.2574	+	4.18920i	1.08849	+	0.236787i	0.720789	−	0.693155i	$-0.243780\pi$
$313$	19.2574	+	4.18920i	1.08849	+	0.236787i	0.367705	+	0.929942i	$0.380144\pi$
$314$	−19.0961	−	5.60712i	−1.07766	−	0.316428i
$315$	20.0455	−	19.2719i	1.12943	−	1.08585i
$316$	−3.67733	+	3.18642i	−0.206866	+	0.179250i
$317$	2.28588	+	10.5080i	0.128388	+	0.590188i	0.995717	+	0.0924537i	$0.0294710\pi$
$317$	2.28588	+	10.5080i	0.128388	+	0.590188i	−0.867329	+	0.497735i	$0.834165\pi$
$318$	3.79588	−	0.271487i	0.212862	−	0.0152242i
$319$	0.989263	−	0.290474i	0.0553881	−	0.0162634i
$320$	−2.15747	+	0.587645i	−0.120606	+	0.0328503i
$321$		−	38.5336i		−	2.15074i
$322$	12.6873	−	0.344589i	0.707038	−	0.0192032i
$323$	4.81426	−	4.81426i	0.267873	−	0.267873i
$324$	−0.924807	+	0.422345i	−0.0513782	+	0.0234636i
$325$	21.8777	−	20.2204i	1.21355	−	1.12162i
$326$	0.0412661	−	0.0476236i	0.00228552	−	0.00263763i
$327$	−27.9971	+	6.09040i	−1.54824	+	0.336800i
$328$	9.15484	+	0.654767i	0.505492	+	0.0361535i
$329$	1.48551	+	10.3319i	0.0818988	+	0.569619i
$330$	3.69540	−	7.68786i	0.203425	−	0.423203i
$331$	−3.02903	+	1.94664i	−0.166491	+	0.106997i	−0.621233	−	0.783626i	$-0.713368\pi$
$331$	−3.02903	+	1.94664i	−0.166491	+	0.106997i	0.454742	+	0.890623i	$0.349731\pi$
$332$	0.142460	+	0.190305i	0.00781852	+	0.0104443i
$333$	26.4749	−	9.87461i	1.45081	−	0.541125i
$334$	1.54625	+	0.706147i	0.0846068	+	0.0386387i
$335$	−3.42499	−	6.57677i	−0.187127	−	0.359327i
$336$	3.97001	+	6.17746i	0.216582	+	0.337008i
$337$	19.8009	−	10.8121i	1.07862	−	0.588972i	0.161214	−	0.986919i	$-0.448459\pi$
$337$	19.8009	−	10.8121i	1.07862	−	0.588972i	0.917408	+	0.397947i	$0.130277\pi$
$338$	18.0120	+	13.4836i	0.979726	+	0.733413i
$339$	−25.3707	−	29.2794i	−1.37795	−	1.59024i
$340$	−0.199995	−	3.86295i	−0.0108462	−	0.209498i
$341$	8.77926	+	7.60727i	0.475424	+	0.411957i
$342$	8.86322	−	16.2318i	0.479268	−	0.877714i
$343$	−6.47041	+	17.3478i	−0.349369	+	0.936695i
$344$	−10.8544			−0.585228
$345$	−29.1218	−	6.10730i	−1.56787	−	0.328806i
$346$	−9.37399			−0.503949
$347$	2.79801	−	7.50174i	0.150205	−	0.402715i	−0.839955	−	0.542656i	$-0.817419\pi$
$347$	2.79801	−	7.50174i	0.150205	−	0.402715i	0.990160	+	0.139941i	$0.0446914\pi$
$348$	0.997249	−	1.82633i	0.0534582	−	0.0979013i
$349$	13.6277	+	11.8085i	0.729474	+	0.632092i	0.938285	−	0.345864i	$-0.112414\pi$
$349$	13.6277	+	11.8085i	0.729474	+	0.632092i	−0.208811	+	0.977956i	$0.566959\pi$
$350$	−8.26526	−	10.3335i	−0.441797	−	0.552347i
$351$	−18.3933	−	21.2270i	−0.981763	−	1.13301i
$352$	1.10059	+	0.823894i	0.0586618	+	0.0439137i
$353$	−5.19035	+	2.83415i	−0.276255	+	0.150846i	−0.611404	−	0.791319i	$-0.709395\pi$
$353$	−5.19035	+	2.83415i	−0.276255	+	0.150846i	0.335149	+	0.942165i	$0.391213\pi$
$354$	−12.6358	−	19.6617i	−0.671586	−	1.04501i
$355$	−9.07987	+	28.8137i	−0.481910	+	1.52927i
$356$	−11.1408	−	5.08782i	−0.590460	−	0.269654i
$357$	−11.9019	+	4.43916i	−0.629913	+	0.234945i
$358$	−1.34061	−	1.79084i	−0.0708534	−	0.0946491i
$359$	20.9720	−	13.4779i	1.10686	−	0.711336i	0.146253	−	0.989247i	$-0.453279\pi$
$359$	20.9720	−	13.4779i	1.10686	−	0.711336i	0.960607	+	0.277912i	$0.0896422\pi$
$360$	−3.47751	−	9.91503i	−0.183281	−	0.522568i
$361$	0.499492	+	3.47404i	0.0262891	+	0.182844i
$362$	12.3885	+	0.886045i	0.651127	+	0.0465695i
$363$	24.6995	−	5.37306i	1.29639	−	0.282012i
$364$	10.3259	−	11.9168i	0.541226	−	0.624608i
$365$	−20.1153	+	25.7971i	−1.05288	+	1.35028i
$366$	1.26476	−	0.577596i	0.0661100	−	0.0301914i
$367$	−13.6622	+	13.6622i	−0.713159	+	0.713159i	−0.967195	−	0.254036i	$-0.918242\pi$
$367$	−13.6622	+	13.6622i	−0.713159	+	0.713159i	0.254036	+	0.967195i	$0.418242\pi$
$368$	1.87309	−	4.41492i	0.0976413	−	0.230144i
$369$			43.1281i			2.24516i
$370$	−3.53371	−	12.9736i	−0.183709	−	0.674465i
$371$	−3.48268	+	1.02261i	−0.180812	+	0.0530911i
$372$	23.3854	−	1.67256i	1.21248	−	0.0867180i
$373$	−6.11554	−	28.1127i	−0.316651	−	1.45562i	−0.810329	−	0.585975i	$-0.800712\pi$
$373$	−6.11554	−	28.1127i	−0.316651	−	1.45562i	0.493679	−	0.869644i	$-0.335652\pi$
$374$	−1.79737	+	1.55743i	−0.0929396	+	0.0805326i
$375$	13.2354	+	28.0570i	0.683472	+	1.44886i
$376$	3.78443	+	1.11121i	0.195167	+	0.0573062i
$377$	−4.36616	−	0.949800i	−0.224869	−	0.0489172i
$378$	−9.98731	+	7.47641i	−0.513692	+	0.384545i
$379$	−4.91280	+	10.7575i	−0.252354	+	0.552577i	−0.992834	−	0.119500i	$-0.961871\pi$
$379$	−4.91280	+	10.7575i	−0.252354	+	0.552577i	0.740481	+	0.672078i	$0.234598\pi$
$380$	−7.30853	−	4.90271i	−0.374920	−	0.251503i
$381$	−6.19694	+	43.1007i	−0.317479	+	2.20811i
$382$	−2.58971	+	11.9047i	−0.132501	+	0.609097i
$383$	7.22506	+	13.2317i	0.369183	+	0.676108i	0.994554	−	0.104219i	$-0.0332343\pi$
$383$	7.22506	+	13.2317i	0.369183	+	0.676108i	−0.625371	+	0.780327i	$0.715052\pi$
$384$	2.74646	−	0.394881i	0.140155	−	0.0201512i
$385$	−1.88542	+	7.91422i	−0.0960901	+	0.403346i
$386$	2.78532	+	1.79002i	0.141769	+	0.0911095i
$387$	−3.63860	−	50.8742i	−0.184960	−	2.58608i
$388$	5.45415	+	2.97819i	0.276892	+	0.151195i
$389$	−3.34366	−	7.32159i	−0.169530	−	0.371219i	0.805729	−	0.592285i	$-0.201774\pi$
$389$	−3.34366	−	7.32159i	−0.169530	−	0.371219i	−0.975259	+	0.221065i	$0.929047\pi$
$390$	−30.0237	+	21.5670i	−1.52031	+	1.09209i
$391$	6.77399	+	4.78958i	0.342575	+	0.242220i
$392$	−0.00269014	−	0.00269014i	−0.000135873	−	0.000135873i
$393$	12.6963	+	4.73548i	0.640445	+	0.238874i
$394$	−5.03976	−	17.1638i	−0.253899	−	0.864701i
$395$	−8.36133	+	6.96192i	−0.420704	+	0.350292i
$396$	−3.49264	+	5.43465i	−0.175512	+	0.273101i
$397$	−1.47296	+	20.5946i	−0.0739256	+	1.03361i	0.816162	+	0.577824i	$0.196098\pi$
$397$	−1.47296	+	20.5946i	−0.0739256	+	1.03361i	−0.890087	+	0.455790i	$0.849357\pi$
$398$	−13.3283	+	17.8046i	−0.668089	+	0.892462i
$399$	−8.14233	+	27.7302i	−0.407627	+	1.38825i
$400$	−4.84916	+	1.21886i	−0.242458	+	0.0609428i
$401$	−19.4357	−	2.79444i	−0.970574	−	0.139547i	−0.361250	−	0.932469i	$-0.617650\pi$
$401$	−19.4357	−	2.79444i	−0.970574	−	0.139547i	−0.609324	+	0.792921i	$0.708559\pi$
$402$	3.21554	+	8.62119i	0.160376	+	0.429986i
$403$	−17.5935	−	47.1700i	−0.876395	−	2.34971i
$404$	11.9153	+	1.71316i	0.592808	+	0.0852330i
$405$	−2.08611	+	0.903529i	−0.103660	+	0.0448967i
$406$	−0.559153	+	1.90430i	−0.0277503	+	0.0945088i
$407$	−4.95436	+	6.61825i	−0.245578	+	0.328054i
$408$	−0.342420	+	4.78766i	−0.0169523	+	0.237025i
$409$	8.65689	−	13.4704i	0.428056	−	0.666068i	−0.558498	−	0.829506i	$-0.688622\pi$
$409$	8.65689	−	13.4704i	0.428056	−	0.666068i	0.986554	+	0.163438i	$0.0522585\pi$
$410$	20.4381	+	1.86653i	1.00937	+	0.0921812i
$411$	5.92383	+	20.1747i	0.292201	+	0.995146i
$412$	2.81288	+	1.04915i	0.138581	+	0.0516880i
$413$	15.7627	+	15.7627i	0.775632	+	0.775632i
$414$	21.3206	+	7.29915i	1.04785	+	0.358734i
$415$	0.310118	+	0.431718i	0.0152231	+	0.0211922i
$416$	−2.47511	−	5.41974i	−0.121352	−	0.265725i
$417$	−36.9289	−	20.1647i	−1.80842	−	0.987470i
$418$	0.386012	+	5.39715i	0.0188804	+	0.263983i
$419$	−18.4843	−	11.8791i	−0.903016	−	0.580333i	0.00466696	−	0.999989i	$-0.498514\pi$
$419$	−18.4843	−	11.8791i	−0.903016	−	0.580333i	−0.907683	+	0.419656i	$0.862151\pi$
$420$	8.60376	+	13.9852i	0.419821	+	0.682407i
$421$	−23.0779	+	3.31809i	−1.12475	+	0.161714i	−0.679487	−	0.733688i	$-0.737798\pi$
$421$	−23.0779	+	3.31809i	−1.12475	+	0.161714i	−0.445259	+	0.895402i	$0.646888\pi$
$422$	3.95183	+	7.23723i	0.192372	+	0.352303i
$423$	−3.93960	+	18.1100i	−0.191550	+	0.880540i
$424$	−0.195189	+	1.35757i	−0.00947920	+	0.0659293i
$425$	−0.277191	−	8.64495i	−0.0134457	−	0.419342i
$426$	15.5730	−	34.1000i	0.754512	−	1.65215i
$427$	−1.06164	+	0.794732i	−0.0513763	+	0.0384598i
$428$	13.5701	+	2.95200i	0.655937	+	0.142690i
$429$	21.8079	+	6.40338i	1.05290	+	0.309158i
$430$	−24.2664	−	0.477466i	−1.17023	−	0.0230255i
$431$	−0.824252	+	0.714218i	−0.0397028	+	0.0344027i	−0.674486	−	0.738287i	$-0.735635\pi$
$431$	−0.824252	+	0.714218i	−0.0397028	+	0.0344027i	0.634783	+	0.772690i	$0.281089\pi$
$432$	1.00205	+	4.60636i	0.0482113	+	0.221624i
$433$	−20.5028	+	1.46639i	−0.985302	+	0.0704702i	−0.554682	−	0.832063i	$-0.687160\pi$
$433$	−20.5028	+	1.46639i	−0.985302	+	0.0704702i	−0.430621	+	0.902533i	$0.641705\pi$
$434$	−21.4558	+	6.30001i	−1.02991	+	0.302410i
$435$	2.30982	−	4.03913i	0.110748	−	0.193661i
$436$		−	10.3261i		−	0.494532i
$437$	17.9596	−	5.80752i	0.859125	−	0.277811i
$438$	28.7033	−	28.7033i	1.37149	−	1.37149i
$439$	16.3568	−	7.46989i	0.780666	−	0.356518i	0.0151087	−	0.999886i	$-0.495191\pi$
$439$	16.3568	−	7.46989i	0.780666	−	0.356518i	0.765557	+	0.643368i	$0.222463\pi$
$440$	2.42428	+	1.89034i	0.115573	+	0.0901184i
$441$	0.0117068	−	0.0135104i	0.000557469	−	0.000643354i
$442$	10.0714	−	2.19089i	0.479046	−	0.104210i
$443$	−27.7898	−	1.98757i	−1.32033	−	0.0944322i	−0.606689	−	0.794939i	$-0.707503\pi$
$443$	−27.7898	−	1.98757i	−1.32033	−	0.0944322i	−0.713646	+	0.700507i	$0.752957\pi$
$444$	2.37455	+	16.5154i	0.112691	+	0.783785i
$445$	−24.6829	−	11.8646i	−1.17008	−	0.562435i
$446$	13.3587	−	8.58515i	0.632555	−	0.406518i
$447$	26.2170	+	35.0219i	1.24002	+	1.65648i
$448$	−2.47961	+	0.924847i	−0.117151	+	0.0436949i
$449$	6.54884	+	2.99076i	0.309059	+	0.141142i	0.563906	−	0.825839i	$-0.309298\pi$
$449$	6.54884	+	2.99076i	0.309059	+	0.141142i	−0.254847	+	0.966981i	$0.582025\pi$
$450$	−7.33829	−	22.3194i	−0.345930	−	1.05215i
$451$	−6.82199	−	10.6152i	−0.321235	−	0.499851i
$452$	12.2547	−	6.69159i	0.576414	−	0.314746i
$453$	6.32952	+	4.73822i	0.297387	+	0.222621i
$454$	14.4989	+	16.7326i	0.680465	+	0.785299i
$455$	23.6092	−	26.1873i	1.10682	−	1.22768i
$456$	8.25321	+	7.15145i	0.386492	+	0.334897i
$457$	16.8589	−	30.8748i	0.788627	−	1.44426i	−0.104533	−	0.994521i	$-0.533335\pi$
$457$	16.8589	−	30.8748i	0.788627	−	1.44426i	0.893159	−	0.449740i	$-0.148483\pi$
$458$	−3.95346	+	10.5996i	−0.184733	+	0.495288i
$459$	−8.15480			−0.380634
$460$	4.38174	−	9.78776i	0.204300	−	0.456357i
$461$	−13.1694			−0.613361			−0.306681	−	0.951813i	$-0.599218\pi$
$461$	−13.1694			−0.613361			−0.306681	+	0.951813i	$0.599218\pi$
$462$	3.52800	−	9.45894i	0.164138	−	0.440070i
$463$	−3.70060	+	6.77715i	−0.171982	+	0.314961i	−0.949426	−	0.313991i	$-0.898334\pi$
$463$	−3.70060	+	6.77715i	−0.171982	+	0.314961i	0.777444	+	0.628952i	$0.216516\pi$
$464$	0.566767	+	0.491106i	0.0263115	+	0.0227990i
$465$	52.3548	−	2.71054i	2.42790	−	0.125698i
$466$	−3.16091	−	3.64789i	−0.146427	−	0.168985i
$467$	29.3961	+	22.0057i	1.36029	+	1.01830i	0.996214	+	0.0869321i	$0.0277063\pi$
$467$	29.3961	+	22.0057i	1.36029	+	1.01830i	0.364077	+	0.931369i	$0.381385\pi$
$468$	24.5725	−	13.4176i	1.13587	−	0.620230i
$469$	−4.74472	−	7.38293i	−0.219091	−	0.340912i
$470$	8.41172	+	2.65073i	0.388004	+	0.122269i
$471$	50.2325	+	22.9404i	2.31459	+	1.05704i
$472$	7.89214	−	2.94362i	0.363265	−	0.135491i
$473$	8.94285	+	11.9462i	0.411193	+	0.549289i
$474$	11.3579	−	7.29927i	0.521685	−	0.335266i
$475$	−16.1235	−	11.2822i	−0.739799	−	0.517661i
$476$	−0.651527	−	4.53147i	−0.0298627	−	0.207700i
$477$	−6.42833	−	0.459763i	−0.294333	−	0.0210511i
$478$	−7.24207	+	1.57542i	−0.331245	+	0.0720579i
$479$	−0.844566	+	0.974681i	−0.0385892	+	0.0445343i	−0.774716	−	0.632309i	$-0.782107\pi$
$479$	−0.844566	+	0.974681i	−0.0385892	+	0.0445343i	0.736127	+	0.676844i	$0.236653\pi$
$480$	6.15745	−	0.761997i	0.281048	−	0.0347803i
$481$	32.5908	−	14.8837i	1.48601	−	0.678639i
$482$	−4.53033	+	4.53033i	−0.206351	+	0.206351i
$483$	−34.9813	−	4.06359i	−1.59171	−	0.184900i
$484$			9.10989i			0.414086i
$485$	12.0625	+	6.89807i	0.547729	+	0.313225i
$486$	16.2761	−	4.77910i	0.738300	−	0.216785i
$487$	−23.4030	+	1.67381i	−1.06049	+	0.0758477i	−0.590669	−	0.806914i	$-0.701136\pi$
$487$	−23.4030	+	1.67381i	−1.06049	+	0.0758477i	−0.469821	+	0.882762i	$0.655682\pi$
$488$	0.106517	+	0.489650i	0.00482179	+	0.0221654i
$489$	−0.132141	+	0.114501i	−0.00597563	+	0.00517792i
$490$	−0.00589583	−	0.00613250i	−0.000266347	−	0.000277038i
$491$	−21.4094	−	6.28635i	−0.966191	−	0.283699i	−0.239678	−	0.970852i	$-0.577042\pi$
$491$	−21.4094	−	6.28635i	−0.966191	−	0.283699i	−0.726512	+	0.687153i	$0.758860\pi$
$492$	−24.8848	−	5.41336i	−1.12189	−	0.244053i
$493$	−1.03855	+	0.777446i	−0.0467738	+	0.0350144i
$494$	9.74146	−	21.3308i	0.438289	−	0.959719i
$495$	−8.04732	+	11.9963i	−0.361700	+	0.539192i
$496$	−1.20251	+	8.36361i	−0.0539941	+	0.375537i
$497$	−7.60033	+	34.9382i	−0.340921	+	1.56719i
$498$	−0.316113	−	0.578918i	−0.0141654	−	0.0259419i
$499$	8.79665	−	1.26477i	0.393792	−	0.0566187i	0.0574253	−	0.998350i	$-0.481711\pi$
$499$	8.79665	−	1.26477i	0.393792	−	0.0566187i	0.336367	+	0.941731i	$0.390802\pi$
$500$	−10.8946	+	2.51161i	−0.487220	+	0.112323i
$501$	−3.96786	−	2.54999i	−0.177271	−	0.113925i
$502$	−1.26223	−	17.6483i	−0.0563362	−	0.787683i
$503$	−21.6397	−	11.8162i	−0.964865	−	0.526856i	−0.0820762	−	0.996626i	$-0.526155\pi$
$503$	−21.6397	−	11.8162i	−0.964865	−	0.526856i	−0.882789	+	0.469770i	$0.844337\pi$
$504$	−5.16595	−	11.3119i	−0.230110	−	0.503870i
$505$	26.5629	+	4.35414i	1.18203	+	0.193757i
$506$	−6.40226	+	1.57592i	−0.284615	+	0.0700583i
$507$	−44.1448	−	44.1448i	−1.96054	−	1.96054i
$508$	−14.7037	−	5.48421i	−0.652372	−	0.243322i
$509$	−5.02208	−	17.1036i	−0.222600	−	0.758104i	−0.992745	−	0.120236i	$-0.961635\pi$
$509$	−5.02208	−	17.1036i	−0.222600	−	0.758104i	0.770146	−	0.637868i	$-0.220183\pi$
$510$	−0.976128	+	10.6884i	−0.0432237	+	0.473290i
$511$	−20.9318	+	32.5705i	−0.925967	+	1.44083i
$512$	−0.0713392	+	0.997452i	−0.00315278	+	0.0440816i
$513$	−11.1187	+	14.8529i	−0.490904	+	0.655771i
$514$	3.53764	−	12.0481i	0.156039	−	0.531419i
$515$	6.24243	+	2.46925i	0.275074	+	0.108808i
$516$	29.8110	+	4.28618i	1.31236	+	0.188689i
$517$	−1.89498	−	5.08063i	−0.0833410	−	0.223446i
$518$	−5.56142	−	14.9107i	−0.244355	−	0.655140i
$519$	25.7453	+	3.70161i	1.13009	+	0.162483i
$520$	−5.29505	−	12.2254i	−0.232203	−	0.536121i
$521$	−2.58096	+	8.78993i	−0.113074	+	0.385094i	−0.996512	−	0.0834546i	$-0.973405\pi$
$521$	−2.58096	+	8.78993i	−0.113074	+	0.385094i	0.883438	+	0.468548i	$0.155223\pi$
$522$	−2.11182	+	2.82106i	−0.0924317	+	0.123474i
$523$	0.0930148	−	1.30052i	0.00406725	−	0.0568676i	−0.995013	−	0.0997440i	$-0.968198\pi$
$523$	0.0930148	−	1.30052i	0.00406725	−	0.0568676i	0.999080	+	0.0428764i	$0.0136522\pi$
$524$	−2.64031	+	4.10840i	−0.115342	+	0.179476i
$525$	18.6197	+	31.6442i	0.812630	+	1.38107i
$526$	7.31344	+	24.9073i	0.318881	+	1.08601i
$527$	−13.6952	−	5.10805i	−0.596573	−	0.222510i
$528$	−2.69739	−	2.69739i	−0.117389	−	0.117389i
$529$	10.6761	+	20.3721i	0.464177	+	0.885742i
$530$	−0.496088	+	3.02644i	−0.0215487	+	0.131460i
$531$	16.4423	+	36.0036i	0.713535	+	1.56242i
$532$	−9.14180	−	4.99180i	−0.396347	−	0.216422i
$533$	3.90122	+	54.5461i	0.168980	+	2.36266i
$534$	28.5886	+	18.3728i	1.23715	+	0.795067i
$535$	30.2080	+	7.19652i	1.30601	+	0.311133i
$536$	−3.28240	+	0.471938i	−0.141778	+	0.0203846i
$537$	2.97476	+	5.44786i	0.128370	+	0.235092i
$538$	−2.16861	+	9.96895i	−0.0934955	+	0.429792i
$539$	−0.000744360		0.00517714i	−3.20619e−5		0.000222995i
$540$	2.03760	+	10.3422i	0.0876842	+	0.445058i
$541$	4.91854	−	10.7701i	0.211464	−	0.463042i	−0.773943	−	0.633255i	$-0.781718\pi$
$541$	4.91854	−	10.7701i	0.211464	−	0.463042i	0.985407	+	0.170213i	$0.0544456\pi$
$542$	−2.10370	+	1.57481i	−0.0903618	+	0.0676440i
$543$	−33.6747	−	7.32548i	−1.44512	−	0.314366i
$544$	−1.65981	−	0.487363i	−0.0711636	−	0.0208955i
$545$	0.454230	−	23.0855i	0.0194571	−	0.988872i
$546$	−33.0654	+	28.6513i	−1.41507	+	1.22616i
$547$	−6.46661	−	29.7265i	−0.276492	−	1.27101i	−0.880504	−	0.474038i	$-0.842796\pi$
$547$	−6.46661	−	29.7265i	−0.276492	−	1.27101i	0.604012	−	0.796975i	$-0.293568\pi$
$548$	−7.55861	+	0.540603i	−0.322888	+	0.0230934i
$549$	−2.25927	+	0.663383i	−0.0964235	+	0.0283125i
$550$	5.33666	+	4.33275i	0.227556	+	0.184749i
$551$			2.95159i			0.125742i
$552$	−6.88772	+	11.3858i	−0.293161	+	0.484610i
$553$	−9.10555	+	9.10555i	−0.387208	+	0.387208i
$554$	−2.63080	+	1.20144i	−0.111772	+	0.0510445i
$555$	4.58215	+	37.0268i	0.194501	+	1.57170i
$556$	9.93034	−	11.4602i	0.421140	−	0.486022i
$557$	−8.44802	+	1.83775i	−0.357954	+	0.0778681i	−0.387946	−	0.921682i	$-0.626815\pi$
$557$	−8.44802	+	1.83775i	−0.357954	+	0.0778681i	0.0299923	+	0.999550i	$0.490452\pi$
$558$	−39.6032	−	2.83248i	−1.67654	−	0.119908i
$559$	−9.20381	−	64.0139i	−0.389280	−	2.70750i
$560$	−5.58418	+	1.95855i	−0.235975	+	0.0827637i
$561$	5.55139	−	3.56766i	0.234380	−	0.150627i
$562$	−12.2801	−	16.4043i	−0.518004	−	0.691973i
$563$	4.21999	−	1.57398i	0.177851	−	0.0663352i	−0.258961	−	0.965888i	$-0.583380\pi$
$563$	4.21999	−	1.57398i	0.177851	−	0.0663352i	0.436812	+	0.899553i	$0.356107\pi$
$564$	−9.95497	−	4.54628i	−0.419180	−	0.191433i
$565$	27.6915	−	14.4209i	1.16499	−	0.606691i
$566$	2.28089	+	3.54914i	0.0958730	+	0.149181i
$567$	−2.36150	+	1.28948i	−0.0991737	+	0.0541529i
$568$	10.8158	+	8.09657i	0.453819	+	0.339725i
$569$	3.67330	+	4.23922i	0.153993	+	0.177717i	0.827504	−	0.561460i	$-0.189760\pi$
$569$	3.67330	+	4.23922i	0.153993	+	0.177717i	−0.673511	+	0.739177i	$0.735215\pi$
$570$	18.1366	+	16.3511i	0.759658	+	0.684871i
$571$	3.34028	+	2.89437i	0.139786	+	0.121125i	0.721947	−	0.691948i	$-0.243247\pi$
$571$	3.34028	+	2.89437i	0.139786	+	0.121125i	−0.582161	+	0.813073i	$0.697793\pi$
$572$	−3.92570	+	7.18939i	−0.164142	+	0.300603i
$573$	11.8134	−	31.6731i	0.493514	−	1.32316i
$574$	24.2899			1.01384
$575$	10.2265	−	21.6891i	0.426475	−	0.904499i
$576$	−4.69896			−0.195790
$577$	11.4101	−	30.5917i	0.475009	−	1.27355i	−0.449804	−	0.893127i	$-0.648506\pi$
$577$	11.4101	−	30.5917i	0.475009	−	1.27355i	0.924813	−	0.380422i	$-0.124221\pi$
$578$	−6.71309	+	12.2941i	−0.279228	+	0.511367i
$579$	−6.94292	−	6.01608i	−0.288538	−	0.250020i
$580$	1.24548	+	1.12287i	0.0517158	+	0.0466245i
$581$	0.411985	+	0.475456i	0.0170920	+	0.0197252i
$582$	−13.8036	−	10.3332i	−0.572176	−	0.428325i
$583$	1.65494	−	0.903668i	0.0685408	−	0.0374261i
$584$	7.90932	+	12.3071i	0.327290	+	0.509273i
$585$	55.5255	−	28.9160i	2.29570	−	1.19553i
$586$	−6.79454	−	3.10296i	−0.280680	−	0.128182i
$587$	29.9887	−	11.1852i	1.23776	−	0.461662i	0.356504	−	0.934294i	$-0.383968\pi$
$587$	29.9887	−	11.1852i	1.23776	−	0.461662i	0.881260	+	0.472631i	$0.156696\pi$
$588$	0.00632607	+	0.00845064i	0.000260883	+	0.000348498i
$589$	−27.9765	+	17.9794i	−1.15275	+	0.740827i
$590$	17.7734	−	6.23369i	0.731721	−	0.256637i
$591$	7.06380	+	49.1298i	0.290566	+	2.02093i
$592$	−5.99802	−	0.428987i	−0.246517	−	0.0176313i
$593$	−1.26290	+	0.274726i	−0.0518610	+	0.0112817i	−0.238421	−	0.971162i	$-0.576630\pi$
$593$	−1.26290	+	0.274726i	−0.0518610	+	0.0112817i	0.186560	+	0.982444i	$0.440266\pi$
$594$	4.24414	−	4.89800i	0.174139	−	0.200968i
$595$	−1.25725	−	10.1594i	−0.0515420	−	0.416494i
$596$	−14.3419	+	6.54971i	−0.587466	+	0.268287i
$597$	43.6364	−	43.6364i	1.78592	−	1.78592i
$598$	27.6254	+	7.30300i	1.12969	+	0.298642i
$599$		−	28.2374i		−	1.15375i	−0.816832	−	0.576875i	$-0.804272\pi$
$599$		−	28.2374i		−	1.15375i	0.816832	−	0.576875i	$-0.195728\pi$
$600$	13.7993	−	1.43269i	0.563355	−	0.0584894i
$601$	25.7171	−	7.55122i	1.04902	−	0.308021i	0.288600	−	0.957450i	$-0.406810\pi$
$601$	25.7171	−	7.55122i	1.04902	−	0.308021i	0.760422	+	0.649429i	$0.224992\pi$
$602$	−28.6526	+	2.04927i	−1.16779	+	0.0835221i
$603$	−3.31229	−	15.2264i	−0.134887	−	0.620065i
$604$	−2.15352	+	1.86604i	−0.0876255	+	0.0759279i
$605$	−0.400729	+	20.3664i	−0.0162920	+	0.828012i
$606$	−32.0484	−	9.41025i	−1.30188	−	0.382265i
$607$	26.4093	+	5.74499i	1.07192	+	0.233182i	0.713697	−	0.700454i	$-0.247019\pi$
$607$	26.4093	+	5.74499i	1.07192	+	0.233182i	0.358222	+	0.933636i	$0.383383\pi$
$608$	−3.15074	+	2.35861i	−0.127779	+	0.0956545i
$609$	2.28766	−	5.00928i	0.0927007	−	0.202986i
$610$	0.216594	+	1.09936i	0.00876963	+	0.0445119i
$611$	−3.34443	+	23.2610i	−0.135301	+	0.941039i
$612$	1.72786	−	7.94286i	0.0698447	−	0.321071i
$613$	18.0806	+	33.1121i	0.730269	+	1.33739i	0.933614	+	0.358280i	$0.116637\pi$
$613$	18.0806	+	33.1121i	0.730269	+	1.33739i	−0.203346	+	0.979107i	$0.565181\pi$
$614$	−21.1596	+	3.04229i	−0.853931	+	0.122777i
$615$	−55.3953	−	13.1969i	−2.23375	−	0.532152i
$616$	3.06082	+	1.96707i	0.123324	+	0.0792554i
$617$	1.39525	+	19.5082i	0.0561707	+	0.785369i	0.944988	+	0.327106i	$0.106074\pi$
$617$	1.39525	+	19.5082i	0.0561707	+	0.785369i	−0.888817	+	0.458263i	$0.848472\pi$
$618$	−7.31117	−	3.99220i	−0.294098	−	0.160590i
$619$	3.87216	+	8.47884i	0.155635	+	0.340793i	0.971347	−	0.237665i	$-0.0763819\pi$
$619$	3.87216	+	8.47884i	0.155635	+	0.340793i	−0.815712	+	0.578458i	$0.803655\pi$
$620$	−3.05627	+	18.6451i	−0.122743	+	0.748805i
$621$	−20.1294	−	10.2921i	−0.807765	−	0.413009i
$622$	19.8845	+	19.8845i	0.797297	+	0.797297i
$623$	−30.3692	−	11.3271i	−1.21671	−	0.453811i
$624$	4.65764	+	15.8625i	0.186455	+	0.635007i
$625$	−24.4668	+	5.13581i	−0.978671	+	0.205432i
$626$	10.6548	−	16.5793i	0.425853	−	0.662641i
$627$	1.07107	−	14.9755i	0.0427743	−	0.598062i
$628$	−11.9270	+	15.9326i	−0.475939	+	0.635780i
$629$	2.93068	−	9.98098i	0.116854	−	0.397968i
$630$	−11.0516	−	25.5164i	−0.440306	−	1.01660i
$631$	6.50840	+	0.935767i	0.259095	+	0.0372523i	0.270638	−	0.962681i	$-0.412765\pi$
$631$	6.50840	+	0.935767i	0.259095	+	0.0372523i	−0.0115430	+	0.999933i	$0.503674\pi$
$632$	1.70042	+	4.55901i	0.0676392	+	0.181348i
$633$	−7.99568	−	21.4373i	−0.317800	−	0.852054i
$634$	10.6443	+	1.53042i	0.422739	+	0.0607807i
$635$	−32.6309	−	12.9075i	−1.29492	−	0.512218i
$636$	1.07215	−	3.65142i	0.0425137	−	0.144788i
$637$	0.0135841	−	0.0181462i	0.000538222	−	0.000718980i
$638$	0.0735526	−	1.02840i	0.00291197	−	0.0407147i
$639$	−34.3228	+	53.4074i	−1.35779	+	2.11276i
$640$	−0.203365	+	2.22680i	−0.00803870	+	0.0880220i
$641$	7.31588	+	24.9156i	0.288960	+	0.984107i	0.968197	+	0.250188i	$0.0804926\pi$
$641$	7.31588	+	24.9156i	0.288960	+	0.984107i	−0.679237	+	0.733919i	$0.737689\pi$
$642$	−36.1041	−	13.4661i	−1.42491	−	0.531466i
$643$	−5.77968	−	5.77968i	−0.227928	−	0.227928i	0.583898	−	0.811827i	$-0.301527\pi$
$643$	−5.77968	−	5.77968i	−0.227928	−	0.227928i	−0.811827	+	0.583898i	$0.801527\pi$
$644$	4.11091	−	12.0078i	0.161993	−	0.473175i
$645$	66.4581	+	10.8937i	2.61678	+	0.428938i
$646$	−2.82831	−	6.19313i	−0.111278	−	0.243665i
$647$	−6.42125	−	3.50627i	−0.252445	−	0.137846i	0.348044	−	0.937478i	$-0.386846\pi$
$647$	−6.42125	−	3.50627i	−0.252445	−	0.137846i	−0.600490	+	0.799632i	$0.705028\pi$
$648$	0.0725293	+	1.01409i	0.00284922	+	0.0398373i
$649$	−9.74202	−	6.26081i	−0.382408	−	0.245758i
$650$	−11.3000	−	27.5646i	−0.443223	−	1.08117i
$651$	61.4153	−	8.83019i	2.40706	−	0.346082i
$652$	−0.0301999	−	0.0553070i	−0.00118272	−	0.00216599i
$653$	6.97209	−	32.0502i	0.272839	−	1.25422i	−0.612946	−	0.790124i	$-0.710016\pi$
$653$	6.97209	−	32.0502i	0.272839	−	1.25422i	0.885785	−	0.464095i	$-0.153620\pi$
$654$	−4.07759	+	28.3603i	−0.159446	+	1.10897i
$655$	−6.08349	+	9.06874i	−0.237702	+	0.354345i
$656$	3.81277	−	8.34881i	0.148864	−	0.325966i
$657$	−55.0320	+	41.1964i	−2.14700	+	1.60723i
$658$	10.1996	+	2.21880i	0.397624	+	0.0864977i
$659$	8.88229	+	2.60807i	0.346005	+	0.101596i	0.450117	−	0.892969i	$-0.351382\pi$
$659$	8.88229	+	2.60807i	0.346005	+	0.101596i	−0.104113	+	0.994565i	$0.533200\pi$
$660$	−5.91173	−	6.14904i	−0.230114	−	0.239351i
$661$	34.6672	−	30.0393i	1.34840	−	1.16839i	0.378298	−	0.925684i	$-0.376509\pi$
$661$	34.6672	−	30.0393i	1.34840	−	1.16839i	0.970099	−	0.242709i	$-0.0780360\pi$
$662$	0.765366	+	3.51833i	0.0297468	+	0.136744i
$663$	−28.5257	+	2.04020i	−1.10785	+	0.0792348i
$664$	0.228090	−	0.0669734i	0.00885163	−	0.00259907i
$665$	−20.2181	−	11.5620i	−0.784026	−	0.448354i
$666$		−	28.2564i		−	1.09491i
$667$	−3.54477	+	0.608312i	−0.137254	+	0.0235540i
$668$	1.20198	−	1.20198i	0.0465061	−	0.0465061i
$669$	−40.0793	+	18.3036i	−1.54956	+	0.707659i
$670$	−7.35901	+	0.910694i	−0.284303	+	0.0351832i
$671$	0.451147	−	0.520651i	0.0174163	−	0.0200995i
$672$	7.17534	−	1.56090i	0.276795	−	0.0602131i
$673$	3.23635	+	0.231468i	0.124752	+	0.00892243i	0.133576	−	0.991039i	$-0.457354\pi$
$673$	3.23635	+	0.231468i	0.124752	+	0.00892243i	−0.00882359	+	0.999961i	$0.502809\pi$
$674$	−3.21069	−	22.3309i	−0.123671	−	0.860153i
$675$	4.10039	+	23.2111i	0.157824	+	0.893394i
$676$	18.9281	−	12.1643i	0.728002	−	0.467859i
$677$	−18.6109	−	24.8613i	−0.715275	−	0.955496i	0.284720	−	0.958611i	$-0.408099\pi$
$677$	−18.6109	−	24.8613i	−0.715275	−	0.955496i	−0.999995	+	0.00311468i	$0.999009\pi$
$678$	−36.2995	+	13.5390i	−1.39407	+	0.519962i
$679$	14.9597	+	6.83188i	0.574102	+	0.262184i
$680$	−3.68928	−	1.16258i	−0.141478	−	0.0445828i
$681$	−33.2131	−	51.6806i	−1.27273	−	1.98041i
$682$	10.1957	−	5.56726i	0.390412	−	0.213181i
$683$	−8.43127	−	6.31157i	−0.322614	−	0.241505i	0.425679	−	0.904874i	$-0.360035\pi$
$683$	−8.43127	−	6.31157i	−0.322614	−	0.241505i	−0.748293	+	0.663369i	$0.769126\pi$
$684$	−12.1110	−	13.9768i	−0.463075	−	0.534417i
$685$	−16.9221	+	0.876099i	−0.646559	+	0.0334740i
$686$	13.9929	+	12.1249i	0.534250	+	0.462931i
$687$	15.0436	−	27.5503i	0.573949	−	1.05111i
$688$	−3.79321	+	10.1700i	−0.144615	+	0.387727i
$689$	−8.17180			−0.311321
$690$	−15.8993	+	25.1514i	−0.605275	+	0.957498i
$691$	10.0464			0.382184			0.191092	−	0.981572i	$-0.438797\pi$
$691$	10.0464			0.382184			0.191092	+	0.981572i	$0.438797\pi$
$692$	−3.27587	+	8.78296i	−0.124530	+	0.333878i
$693$	−8.19356	+	15.0054i	−0.311248	+	0.570008i
$694$	−6.05095	−	5.24318i	−0.229691	−	0.199028i
$695$	22.7047	−	25.1841i	0.861239	−	0.955286i
$696$	−1.36267	−	1.57261i	−0.0516520	−	0.0596095i
$697$	12.7104	+	9.51486i	0.481439	+	0.360401i
$698$	15.8263	−	8.64183i	0.599035	−	0.327098i
$699$	7.24083	+	11.2670i	0.273873	+	0.426155i
$700$	−12.5704	+	4.13295i	−0.475115	+	0.156211i
$701$	−12.4545	−	5.68778i	−0.470400	−	0.214824i	0.166088	−	0.986111i	$-0.446886\pi$
$701$	−12.4545	−	5.68778i	−0.470400	−	0.214824i	−0.636488	+	0.771287i	$0.719614\pi$
$702$	−26.3165	+	9.81553i	−0.993251	+	0.370463i
$703$	−14.1832	−	18.9465i	−0.534928	−	0.714580i
$704$	1.15657	−	0.743279i	0.0435897	−	0.0280134i
$705$	−22.0557	−	10.6017i	−0.830666	−	0.399284i
$706$	0.841611	+	5.85353i	0.0316745	+	0.220301i
$707$	31.7766	+	2.27271i	1.19508	+	0.0854739i
$708$	−22.8378	+	4.96806i	−0.858298	+	0.186711i
$709$	−17.4233	+	20.1075i	−0.654344	+	0.755154i	−0.981842	−	0.189698i	$-0.939249\pi$
$709$	−17.4233	+	20.1075i	−0.654344	+	0.755154i	0.327498	+	0.944852i	$0.393794\pi$
$710$	23.8239	+	18.5767i	0.894096	+	0.697173i
$711$	−20.7980	+	9.49813i	−0.779986	+	0.356208i
$712$	−8.66033	+	8.66033i	−0.324560	+	0.324560i
$713$	−27.3586	−	29.8934i	−1.02459	−	1.11952i
$714$			12.7028i			0.475389i
$715$	−9.09269	+	15.9002i	−0.340047	+	0.594633i
$716$	−2.14643	+	0.630248i	−0.0802157	+	0.0235535i
$717$	20.5121	−	1.46706i	0.766040	−	0.0547882i
$718$	−5.29914	−	24.3597i	−0.197762	−	0.909098i
$719$	18.6160	−	16.1309i	0.694260	−	0.601580i	−0.234564	−	0.972101i	$-0.575366\pi$
$719$	18.6160	−	16.1309i	0.694260	−	0.601580i	0.928824	+	0.370521i	$0.120821\pi$
$720$	−10.5052	−	0.206699i	−0.391504	−	0.00770323i
$721$	7.62332	+	2.23841i	0.283907	+	0.0833627i
$722$	3.42956	+	0.746055i	0.127635	+	0.0277653i
$723$	14.2313	−	10.6534i	0.529267	−	0.396205i
$724$	5.15953	−	11.2978i	0.191752	−	0.419879i
$725$	2.73505	+	2.56510i	0.101577	+	0.0952656i
$726$	3.59732	−	25.0199i	0.133509	−	0.928577i
$727$	1.70348	−	7.83078i	0.0631786	−	0.290428i	−0.934707	−	0.355419i	$-0.884338\pi$
$727$	1.70348	−	7.83078i	0.0631786	−	0.290428i	0.997886	+	0.0649912i	$0.0207019\pi$
$728$	−7.55686	−	13.8394i	−0.280076	−	0.512921i
$729$	−43.5699	+	6.26440i	−1.61370	+	0.232015i
$730$	17.1410	+	27.8622i	0.634416	+	1.03123i
$731$	−15.7960	−	10.1515i	−0.584236	−	0.375466i
$732$	−0.0991904	−	1.38686i	−0.00366618	−	0.0512600i
$733$	13.5697	+	7.40959i	0.501207	+	0.273679i	0.709901	−	0.704301i	$-0.248740\pi$
$733$	13.5697	+	7.40959i	0.501207	+	0.273679i	−0.208695	+	0.977981i	$0.566921\pi$
$734$	8.02632	+	17.5752i	0.296257	+	0.648712i
$735$	0.0137710	+	0.0191708i	0.000507953	+	0.000707126i
$736$	−3.48199	−	3.29784i	−0.128348	−	0.121560i
$737$	3.22376	+	3.22376i	0.118749	+	0.118749i
$738$	40.4089	+	15.0717i	1.48747	+	0.554798i
$739$	−7.79624	−	26.5515i	−0.286789	−	0.976714i	−0.969309	−	0.245847i	$-0.920934\pi$
$739$	−7.79624	−	26.5515i	−0.286789	−	0.976714i	0.682520	−	0.730867i	$-0.260884\pi$
$740$	−13.3905	−	1.22290i	−0.492245	−	0.0449548i
$741$	−35.1776	+	54.7375i	−1.29228	+	2.01083i
$742$	−0.258940	+	3.62046i	−0.00950600	+	0.132911i
$743$	5.77990	−	7.72104i	0.212044	−	0.283258i	−0.681891	−	0.731453i	$-0.738842\pi$
$743$	5.77990	−	7.72104i	0.212044	−	0.283258i	0.893935	+	0.448196i	$0.147933\pi$
$744$	6.60526	−	22.4954i	0.242161	−	0.824723i
$745$	−32.3513	+	14.0119i	−1.18526	+	0.513356i
$746$	−28.4773	−	4.09442i	−1.04263	−	0.149907i
$747$	0.390364	+	1.04661i	0.0142827	+	0.0382933i
$748$	0.831116	+	2.22831i	0.0303886	+	0.0814750i
$749$	36.3788	+	5.23048i	1.32925	+	0.191117i
$750$	30.9133	−	2.59597i	1.12879	−	0.0947913i
$751$	0.475411	−	1.61910i	0.0173480	−	0.0590818i	−0.950364	−	0.311140i	$-0.899289\pi$
$751$	0.475411	−	1.61910i	0.0173480	−	0.0590818i	0.967712	+	0.252058i	$0.0811074\pi$
$752$	2.36367	−	3.15749i	0.0861941	−	0.115142i
$753$	−3.50232	+	48.9688i	−0.127631	+	1.78452i
$754$	−2.41573	+	3.75895i	−0.0879757	+	0.136893i
$755$	−4.89657	+	4.07704i	−0.178204	+	0.148379i
$756$	3.51481	+	11.9703i	0.127832	+	0.435357i
$757$	−36.1088	−	13.4679i	−1.31240	−	0.489499i	−0.406754	−	0.913538i	$-0.633339\pi$
$757$	−36.1088	−	13.4679i	−1.31240	−	0.489499i	−0.905644	+	0.424039i	$0.860612\pi$
$758$	8.36242	+	8.36242i	0.303737	+	0.303737i
$759$	18.2058	−	1.80008i	0.660830	−	0.0653386i
$760$	−7.14766	+	5.13441i	−0.259273	+	0.186245i
$761$	9.29182	+	20.3462i	0.336828	+	0.737551i	0.999940	−	0.0109698i	$-0.00349187\pi$
$761$	9.29182	+	20.3462i	0.336828	+	0.737551i	−0.663112	+	0.748520i	$0.730765\pi$
$762$	38.2175	+	20.8684i	1.38448	+	0.755981i
$763$	−1.94954	−	27.2582i	−0.0705782	−	0.986812i
$764$	10.2491	+	6.58668i	0.370799	+	0.238298i
$765$	4.21226	−	17.6813i	0.152295	−	0.639270i
$766$	14.9223	−	2.14551i	0.539166	−	0.0775204i
$767$	24.0521	+	44.0481i	0.868471	+	1.59049i
$768$	0.589805	−	2.71129i	0.0212827	−	0.0978352i
$769$	4.94990	−	34.4273i	0.178498	−	1.24148i	−0.681742	−	0.731593i	$-0.738777\pi$
$769$	4.94990	−	34.4273i	0.178498	−	1.24148i	0.860240	−	0.509889i	$-0.170314\pi$
$770$	6.75634	+	4.53228i	0.243482	+	0.163332i
$771$	−14.4735	+	31.6926i	−0.521252	+	1.14138i
$772$	2.65053	−	1.98416i	0.0953945	−	0.0714115i
$773$	45.0960	+	9.81004i	1.62199	+	0.352843i	0.929569	−	0.368649i	$-0.120180\pi$
$773$	45.0960	+	9.81004i	1.62199	+	0.352843i	0.692423	+	0.721492i	$0.256543\pi$
$774$	−48.9382	−	14.3695i	−1.75905	−	0.516502i
$775$	−7.65286	+	41.5492i	−0.274899	+	1.49249i
$776$	4.69644	−	4.06949i	0.168592	−	0.146086i
$777$	9.38623	+	43.1478i	0.336729	+	1.54792i
$778$	−8.02845	+	0.574206i	−0.287834	+	0.0205863i
$779$	34.6601	−	10.1771i	1.24183	−	0.364633i
$780$	9.71502	+	35.6676i	0.347854	+	1.27710i
$781$		−	18.5745i		−	0.664647i
$782$	6.85486	−	4.67310i	0.245129	−	0.167110i
$783$	2.49982	−	2.49982i	0.0893364	−	0.0893364i
$784$	−0.00346063	+	0.00158042i	−0.000123594	+	5.64435e-5i
$785$	−27.3653	+	35.0948i	−0.976708	+	1.25259i
$786$	8.87382	−	10.2409i	0.316519	−	0.365282i
$787$	−26.8252	+	5.83546i	−0.956214	+	0.208012i	−0.663490	−	0.748185i	$-0.730925\pi$
$787$	−26.8252	+	5.83546i	−0.956214	+	0.208012i	−0.292724	+	0.956197i	$0.594562\pi$
$788$	−17.8429	−	1.27615i	−0.635626	−	0.0454608i
$789$	−10.2506	−	71.2948i	−0.364932	−	2.53816i
$790$	3.60098	+	10.2671i	0.128117	+	0.365287i
$791$	31.0858	−	19.9776i	1.10528	−	0.710323i
$792$	3.87144	+	5.17164i	0.137566	+	0.183766i
$793$	−2.79740	+	1.04338i	−0.0993387	+	0.0370514i
$794$	18.7814	+	8.57717i	0.666526	+	0.304392i
$795$	2.55757	−	8.11609i	0.0907076	−	0.287848i
$796$	12.0242	+	18.7100i	0.426187	+	0.663160i
$797$	5.19296	−	2.83557i	0.183944	−	0.100441i	−0.384638	−	0.923067i	$-0.625674\pi$
$797$	5.19296	−	2.83557i	0.183944	−	0.100441i	0.568582	+	0.822626i	$0.307492\pi$
$798$	23.1364	+	17.3197i	0.819019	+	0.613110i
$799$	4.46810	+	5.15646i	0.158070	+	0.182422i
$800$	−0.552603	+	4.96937i	−0.0195375	+	0.175694i
$801$	−43.4939	−	37.6877i	−1.53678	−	1.33163i
$802$	−9.41034	+	17.2337i	−0.332291	+	0.608545i
$803$	7.02872	−	18.8447i	0.248038	−	0.665016i
$804$	9.20133			0.324506
$805$	9.71870	−	26.6643i	0.342539	−	0.939793i
$806$	−50.3443			−1.77330
$807$	9.89255	−	26.5230i	0.348234	−	0.933652i
$808$	5.76912	−	10.5653i	0.202957	−	0.371688i
$809$	−3.48741	−	3.02186i	−0.122611	−	0.106243i	0.591397	−	0.806380i	$-0.298577\pi$
$809$	−3.48741	−	3.02186i	−0.122611	−	0.106243i	−0.714008	+	0.700138i	$0.753122\pi$
$810$	0.117541	+	2.27033i	0.00412996	+	0.0797713i
$811$	−18.6058	−	21.4722i	−0.653337	−	0.753991i	0.328337	−	0.944561i	$-0.393512\pi$
$811$	−18.6058	−	21.4722i	−0.653337	−	0.753991i	−0.981674	+	0.190570i	$0.938966\pi$
$812$	1.58883	+	1.18938i	0.0557570	+	0.0417392i
$813$	6.39959	−	3.49444i	0.224444	−	0.122555i
$814$	4.46959	+	6.95482i	0.156659	+	0.243766i
$815$	−0.0650831	−	0.124975i	−0.00227976	−	0.00437768i
$816$	4.36613	+	1.99395i	0.152845	+	0.0698021i
$817$	−40.0267	+	14.9292i	−1.40036	+	0.522306i
$818$	−9.59580	−	12.8185i	−0.335509	−	0.448188i
$819$	62.3316	−	40.0581i	2.17804	−	1.39974i
$820$	8.89122	−	18.4972i	0.310495	−	0.645949i
$821$	4.82637	+	33.5681i	0.168441	+	1.17154i	0.882107	+	0.471049i	$0.156125\pi$
$821$	4.82637	+	33.5681i	0.168441	+	1.17154i	−0.713666	+	0.700487i	$0.752966\pi$
$822$	20.9729	+	1.50001i	0.731513	+	0.0523188i
$823$	−2.82513	+	0.614569i	−0.0984777	+	0.0214225i	−0.261534	−	0.965194i	$-0.584228\pi$
$823$	−2.82513	+	0.614569i	−0.0984777	+	0.0214225i	0.163056	+	0.986617i	$0.447865\pi$
$824$	1.96600	−	2.26889i	0.0684890	−	0.0790405i
$825$	−12.9460	−	14.0071i	−0.450722	−	0.487663i
$826$	20.2774	−	9.26036i	0.705540	−	0.322209i
$827$	17.3894	−	17.3894i	0.604688	−	0.604688i	−0.336865	−	0.941553i	$-0.609367\pi$
$827$	17.3894	−	17.3894i	0.604688	−	0.604688i	0.941553	+	0.336865i	$0.109367\pi$
$828$	14.2897	−	17.4255i	0.496602	−	0.605578i
$829$			48.0785i			1.66983i	0.550376	+	0.834917i	$0.314484\pi$
$829$			48.0785i			1.66983i	−0.550376	+	0.834917i	$0.685516\pi$
$830$	0.512873	−	0.139695i	0.0178021	−	0.00484888i
$831$	7.69979	−	2.26086i	0.267103	−	0.0784285i
$832$	−5.94299	+	0.425051i	−0.206036	+	0.0147360i
$833$	−0.00139894	−	0.00643080i	−4.84702e−5	−	0.000222814i
$834$	−31.7987	+	27.5537i	−1.10110	+	0.954107i
$835$	2.74007	−	2.63432i	0.0948239	−	0.0911644i
$836$	5.19175	+	1.52444i	0.179561	+	0.0527237i
$837$	38.9220	+	8.46695i	1.34534	+	0.292661i
$838$	−17.5897	+	13.1675i	−0.607628	+	0.454864i
$839$	1.77280	−	3.88190i	0.0612040	−	0.134018i	−0.876558	−	0.481295i	$-0.840166\pi$
$839$	1.77280	−	3.88190i	0.0612040	−	0.134018i	0.937762	+	0.347277i	$0.112894\pi$
$840$	16.1101	−	3.17397i	0.555852	−	0.109512i
$841$	−4.04709	+	28.1481i	−0.139555	+	0.970625i
$842$	−4.95600	+	22.7823i	−0.170795	+	0.785132i
$843$	27.2490	+	49.9028i	0.938505	+	1.71874i
$844$	8.16195	−	1.17351i	0.280946	−	0.0403939i
$845$	42.8513	−	26.3624i	1.47413	−	0.906893i
$846$	15.5914	+	10.0200i	0.536045	+	0.344495i
$847$	1.71992	+	24.0476i	0.0590972	+	0.826286i
$848$	1.20376	+	0.657303i	0.0413373	+	0.0225719i
$849$	−4.86288	−	10.6482i	−0.166894	−	0.365446i
$850$	−8.19675	−	2.76139i	−0.281146	−	0.0947148i
$851$	19.8311	−	20.9384i	0.679800	−	0.717758i
$852$	−26.5078	−	26.5078i	−0.908143	−	0.908143i
$853$	−3.18390	−	1.18753i	−0.109015	−	0.0406604i	0.294365	−	0.955693i	$-0.404892\pi$
$853$	−3.18390	−	1.18753i	−0.109015	−	0.0406604i	−0.403380	+	0.915033i	$0.632165\pi$
$854$	0.373620	+	1.27243i	0.0127850	+	0.0435417i
$855$	−26.4609	−	31.7798i	−0.904944	−	1.08685i
$856$	7.50815	−	11.6829i	0.256623	−	0.399314i
$857$	−0.797684	+	11.1531i	−0.0272484	+	0.380982i	0.965469	+	0.260517i	$0.0838931\pi$
$857$	−0.797684	+	11.1531i	−0.0272484	+	0.380982i	−0.992718	+	0.120465i	$0.961561\pi$
$858$	13.6207	−	18.1952i	0.465004	−	0.621173i
$859$	3.08930	−	10.5212i	0.105406	−	0.358979i	−0.889852	−	0.456248i	$-0.849193\pi$
$859$	3.08930	−	10.5212i	0.105406	−	0.358979i	0.995258	+	0.0972699i	$0.0310110\pi$
$860$	−8.92760	+	22.5695i	−0.304429	+	0.769615i
$861$	−66.7112	−	9.59162i	−2.27351	−	0.326882i
$862$	0.381140	+	1.02188i	0.0129817	+	0.0348052i
$863$	16.6767	+	44.7119i	0.567680	+	1.52201i	0.830417	+	0.557143i	$0.188102\pi$
$863$	16.6767	+	44.7119i	0.567680	+	1.52201i	−0.262736	+	0.964868i	$0.584625\pi$
$864$	4.66611	+	0.670885i	0.158744	+	0.0228240i
$865$	−7.71001	+	19.4914i	−0.262148	+	0.662727i
$866$	−5.79107	+	19.7226i	−0.196788	+	0.670200i
$867$	23.2919	−	31.1144i	0.791035	−	1.05670i
$868$	−1.59526	+	22.3047i	−0.0541467	+	0.757070i
$869$	3.61665	−	5.62762i	0.122686	−	0.190904i
$870$	−2.97726	−	3.57572i	−0.100939	−	0.121228i
$871$	−5.56654	−	18.9579i	−0.188615	−	0.642363i
$872$	−9.67506	−	3.60861i	−0.327639	−	0.122203i
$873$	20.6480	+	20.6480i	0.698828	+	0.698828i
$874$	0.834890	−	18.8568i	0.0282406	−	0.637840i
$875$	−28.2845	+	8.68683i	−0.956192	+	0.293668i
$876$	−16.8627	−	36.9243i	−0.569739	−	1.24756i
$877$	48.2542	+	26.3488i	1.62943	+	0.889736i	0.992962	+	0.118432i	$0.0377869\pi$
$877$	48.2542	+	26.3488i	1.62943	+	0.889736i	0.636467	+	0.771304i	$0.280395\pi$
$878$	−1.28280	−	17.9359i	−0.0432925	−	0.605308i
$879$	17.4356	+	11.2052i	0.588089	+	0.377942i
$880$	2.61835	−	1.61083i	0.0882647	−	0.0543009i
$881$	0.244909	−	0.0352126i	0.00825120	−	0.00118634i	−0.138188	−	0.990406i	$-0.544128\pi$
$881$	0.244909	−	0.0352126i	0.00825120	−	0.00118634i	0.146439	+	0.989220i	$0.453219\pi$
$882$	−0.00856746	−	0.0156901i	−0.000288482	−	0.000528314i
$883$	−4.32616	+	19.8870i	−0.145587	+	0.669252i	0.845270	+	0.534339i	$0.179439\pi$
$883$	−4.32616	+	19.8870i	−0.145587	+	0.669252i	−0.990857	+	0.134914i	$0.956924\pi$
$884$	1.46683	−	10.2020i	0.0493347	−	0.343131i
$885$	−51.2756	+	10.1022i	−1.72361	+	0.339581i
$886$	−11.5738	+	25.3431i	−0.388830	+	0.851418i
$887$	37.9404	−	28.4018i	1.27391	−	0.953641i	0.273948	−	0.961745i	$-0.411671\pi$
$887$	37.9404	−	28.4018i	1.27391	−	0.953641i	0.999967	+	0.00810398i	$0.00257960\pi$
$888$	16.3039	+	3.54670i	0.547123	+	0.119019i
$889$	−39.8492	−	11.7008i	−1.33650	−	0.392432i
$890$	−19.7423	+	18.9804i	−0.661763	+	0.636224i
$891$	1.05635	−	0.915329i	0.0353889	−	0.0306647i
$892$	−3.37545	−	15.5167i	−0.113018	−	0.519537i
$893$	15.4839	−	1.10743i	0.518148	−	0.0370587i
$894$	41.9757	−	12.3252i	1.40388	−	0.412215i
$895$	−4.82635	+	1.31459i	−0.161327	+	0.0439418i
$896$			2.64647i			0.0884124i
$897$	−72.9881	−	30.9661i	−2.43700	−	1.03393i
$898$	5.09077	−	5.09077i	0.169881	−	0.169881i
$899$	5.76407	−	2.63236i	0.192242	−	0.0877942i
$900$	−23.4766	−	0.924209i	−0.782553	−	0.0308070i
$901$	−1.55371	+	1.79307i	−0.0517615	+	0.0597359i
$902$	−12.3300	+	2.68222i	−0.410543	+	0.0893082i
$903$	79.5023	+	5.68611i	2.64567	+	0.189222i
$904$	−1.98709	−	13.8205i	−0.0660898	−	0.459664i
$905$	12.0318	−	25.0308i	0.399950	−	0.832051i
$906$	6.65141	−	4.27460i	0.220978	−	0.142014i
$907$	20.7612	+	27.7337i	0.689364	+	0.920882i	0.999556	−	0.0297917i	$-0.00948438\pi$
$907$	20.7612	+	27.7337i	0.689364	+	0.920882i	−0.310192	+	0.950674i	$0.600393\pi$
$908$	20.7444	−	7.73727i	0.688428	−	0.256770i
$909$	51.4535	+	23.4980i	1.70661	+	0.779381i
$910$	−16.2856	−	31.2722i	−0.539863	−	1.03666i
$911$	−17.4886	−	27.2128i	−0.579424	−	0.901602i	0.420560	−	0.907265i	$-0.361834\pi$
$911$	−17.4886	−	27.2128i	−0.579424	−	0.901602i	−0.999984	+	0.00566312i	$0.998197\pi$
$912$	9.58475	−	5.23367i	0.317383	−	0.173304i
$913$	−0.261633	−	0.195856i	−0.00865878	−	0.00648188i
$914$	−23.0365	−	26.5856i	−0.761981	−	0.879373i
$915$	−0.160748	−	3.10488i	−0.00531416	−	0.102644i
$916$	8.54973	+	7.40838i	0.282491	+	0.244780i
$917$	−6.19404	+	11.3435i	−0.204545	+	0.374597i
$918$	−2.84981	+	7.64064i	−0.0940578	+	0.252179i
$919$	3.16084			0.104266			0.0521332	−	0.998640i	$-0.483398\pi$
$919$	3.16084			0.104266			0.0521332	+	0.998640i	$0.483398\pi$
$920$	−7.63938	−	7.52594i	−0.251863	−	0.248123i
$921$	59.3152			1.95450
$922$	−4.60224	+	12.3391i	−0.151567	+	0.406366i
$923$	−38.5787	+	70.6516i	−1.26983	+	2.32552i
$924$	−7.62964	−	6.61112i	−0.250997	−	0.217490i
$925$	−29.8825	−	3.32299i	−0.982531	−	0.109259i
$926$	5.05662	+	5.83565i	0.166171	+	0.191771i
$927$	11.2933	+	8.45405i	0.370920	+	0.277667i
$928$	0.658207	−	0.359408i	0.0216067	−	0.0117981i
$929$	−13.0029	−	20.2330i	−0.426612	−	0.663822i	0.559703	−	0.828694i	$-0.310915\pi$
$929$	−13.0029	−	20.2330i	−0.426612	−	0.663822i	−0.986315	+	0.164872i	$0.947279\pi$
$930$	15.7565	−	50.0011i	0.516676	−	1.63960i
$931$	−0.0136202	−	0.00622015i	−0.000446385	−	0.000203857i
$932$	−4.52252	+	1.68681i	−0.148140	+	0.0552533i
$933$	−46.7600	−	62.4640i	−1.53085	−	2.04498i
$934$	30.8911	−	19.8525i	1.01079	−	0.649594i
$935$	1.76005	+	5.01824i	0.0575598	+	0.164114i
$936$	−3.98442	−	27.7122i	−0.130235	−	0.905802i
$937$	−5.55041	−	0.396973i	−0.181324	−	0.0129686i	−0.0196182	−	0.999808i	$-0.506245\pi$
$937$	−5.55041	−	0.396973i	−0.181324	−	0.0129686i	−0.161706	+	0.986839i	$0.551700\pi$
$938$	−8.57554	+	1.86550i	−0.280001	+	0.0609106i
$939$	−35.8099	+	41.3268i	−1.16861	+	1.34865i
$940$	5.42319	−	6.95502i	0.176885	−	0.226848i
$941$	21.2346	−	9.69751i	0.692228	−	0.316130i	−0.0380541	−	0.999276i	$-0.512116\pi$
$941$	21.2346	−	9.69751i	0.692228	−	0.316130i	0.730282	+	0.683146i	$0.239389\pi$
$942$	39.0485	−	39.0485i	1.27227	−	1.27227i
$943$	19.3658	+	39.5283i	0.630636	+	1.28722i
$944$		−	8.42323i		−	0.274153i
$945$	7.33128	+	26.9159i	0.238487	+	0.875576i
$946$	14.3182	−	4.20421i	0.465526	−	0.136691i
$947$	−18.5450	+	1.32637i	−0.602633	+	0.0431012i	−0.369323	−	0.929301i	$-0.620410\pi$
$947$	−18.5450	+	1.32637i	−0.602633	+	0.0431012i	−0.233310	+	0.972402i	$0.574956\pi$
$948$	−2.86987	−	13.1926i	−0.0932091	−	0.428475i
$949$	−65.8751	+	57.0811i	−2.13840	+	1.85293i
$950$	−16.2054	+	11.1642i	−0.525773	+	0.362216i
$951$	−28.6298	−	8.40646i	−0.928384	−	0.272598i
$952$	−4.47345	−	0.973139i	−0.144985	−	0.0315396i
$953$	25.3209	−	18.9550i	0.820226	−	0.614013i	−0.104553	−	0.994519i	$-0.533341\pi$
$953$	25.3209	−	18.9550i	0.820226	−	0.614013i	0.924778	+	0.380506i	$0.124250\pi$
$954$	−2.67724	+	5.86235i	−0.0866790	+	0.189801i
$955$	22.6235	+	15.1763i	0.732078	+	0.491092i
$956$	−1.05476	+	7.33601i	−0.0341133	+	0.237263i
$957$	−0.608104	+	2.79541i	−0.0196572	+	0.0903628i
$958$	0.618082	+	1.13193i	0.0199693	+	0.0365711i
$959$	−19.8506	+	2.85409i	−0.641010	+	0.0921633i
$960$	1.43785	−	6.03551i	0.0464065	−	0.194795i
$961$	33.9833	+	21.8397i	1.09623	+	0.704507i
$962$	−2.55598	−	35.7372i	−0.0824080	−	1.15221i
$963$	57.2745	+	31.2742i	1.84564	+	1.00780i
$964$	2.66150	+	5.82788i	0.0857212	+	0.187703i
$965$	6.01289	−	4.31926i	0.193562	−	0.139042i
$966$	−16.0321	+	31.3557i	−0.515824	+	1.00885i
$967$	−5.16362	−	5.16362i	−0.166051	−	0.166051i	0.619190	−	0.785241i	$-0.287461\pi$
$967$	−5.16362	−	5.16362i	−0.166051	−	0.166051i	−0.785241	+	0.619190i	$0.787461\pi$
$968$	8.53551	+	3.18358i	0.274342	+	0.102324i
$969$	5.32228	+	18.1260i	0.170976	+	0.582291i
$970$	10.6785	−	8.89131i	0.342867	−	0.285483i
$971$	31.0161	−	48.2620i	0.995353	−	1.54880i	0.169025	−	0.985612i	$-0.445938\pi$
$971$	31.0161	−	48.2620i	0.995353	−	1.54880i	0.826329	−	0.563188i	$-0.190425\pi$
$972$	1.21015	−	16.9200i	0.0388154	−	0.542711i
$973$	24.0497	−	32.1267i	0.770999	−	1.02993i
$974$	−6.61022	+	22.5123i	−0.211805	+	0.721342i
$975$	20.1503	+	80.1670i	0.645326	+	2.56740i
$976$	0.496001	+	0.0713142i	0.0158766	+	0.00228271i
$977$	10.3660	+	27.7922i	0.331637	+	0.889152i	0.990577	+	0.136957i	$0.0437322\pi$
$977$	10.3660	+	27.7922i	0.331637	+	0.889152i	−0.658940	+	0.752195i	$0.728995\pi$
$978$	0.0611031	+	0.163824i	0.00195386	+	0.00523850i
$979$	16.6667	+	2.39631i	0.532670	+	0.0765864i
$980$	−0.00780623	+	0.00338101i	−0.000249361	+	0.000108002i
$981$	13.6702	−	46.5565i	0.436457	−	1.48644i
$982$	−13.3718	+	17.8626i	−0.426711	+	0.570019i
$983$	2.01558	−	28.1815i	0.0642871	−	0.898852i	−0.858321	−	0.513113i	$-0.828492\pi$
$983$	2.01558	−	28.1815i	0.0642871	−	0.898852i	0.922608	−	0.385739i	$-0.126053\pi$
$984$	−13.7684	+	21.4241i	−0.438921	+	0.682974i
$985$	−39.8340	−	3.63788i	−1.26922	−	0.115912i
$986$	0.365493	+	1.24475i	0.0116397	+	0.0396411i
$987$	−27.1367	−	10.1215i	−0.863772	−	0.322170i
$988$	−16.5816	−	16.5816i	−0.527532	−	0.527532i
$989$	−26.1789	−	44.9940i	−0.832440	−	1.43073i
$990$	8.42764	+	11.7322i	0.267848	+	0.372874i
$991$	−23.1313	−	50.6504i	−0.734789	−	1.60896i	−0.791941	−	0.610598i	$-0.790929\pi$
$991$	−23.1313	−	50.6504i	−0.734789	−	1.60896i	0.0571516	−	0.998366i	$-0.481798\pi$
$992$	7.41605	+	4.04947i	0.235460	+	0.128571i
$993$	−0.712723	−	9.96517i	−0.0226176	−	0.316235i
$994$	30.0792	+	19.3308i	0.954056	+	0.613134i
$995$	26.0587	+	42.3577i	0.826117	+	1.34283i
$996$	−0.652887	+	0.0938710i	−0.0206875	+	0.00297442i
$997$	−17.9019	−	32.7850i	−0.566960	−	1.03831i	−0.991151	−	0.132738i	$-0.957623\pi$
$997$	−17.9019	−	32.7850i	−0.566960	−	1.03831i	0.424191	−	0.905573i	$-0.360559\pi$
$998$	1.88909	−	8.68401i	0.0597981	−	0.274887i
$999$	−4.03426	+	28.0589i	−0.127638	+	0.887744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.157.7	yes	240
5.3	odd	4	inner	230.2.l.a.203.1	yes	240
23.17	odd	22	inner	230.2.l.a.17.1	✓	240
115.63	even	44	inner	230.2.l.a.63.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.17.1	✓	240	23.17	odd	22	inner
230.2.l.a.63.7	yes	240	115.63	even	44	inner
230.2.l.a.157.7	yes	240	1.1	even	1	trivial
230.2.l.a.203.1	yes	240	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.349464 - 0.936950i) q^{2} +(-1.32977 + 2.43530i) q^{3} +(-0.755750 - 0.654861i) q^{4} +(-1.66077 - 1.49727i) q^{5} +(1.81704 + 2.09698i) q^{6} +(-2.11861 - 1.58597i) q^{7} +(-0.877679 + 0.479249i) q^{8} +(-2.54045 - 3.95301i) q^{9} +(-1.98325 + 1.03282i) q^{10} +(1.25057 + 0.571117i) q^{11} +(2.59975 - 0.969658i) q^{12} +(-3.57060 - 4.76976i) q^{13} +(-2.22635 + 1.43079i) q^{14} +(5.85475 - 2.05344i) q^{15} +(0.142315 + 0.989821i) q^{16} +(-1.72547 - 0.123408i) q^{17} +(-4.59157 + 0.998835i) q^{18} +(-2.57738 + 2.97445i) q^{19} +(0.274623 + 2.21914i) q^{20} +(6.67957 - 3.05046i) q^{21} +(0.972139 - 0.972139i) q^{22} +(-4.10342 - 2.48233i) q^{23} -2.77470i q^{24} +(0.516341 + 4.97327i) q^{25} +(-5.71682 + 1.67861i) q^{26} +(4.70208 - 0.336299i) q^{27} +(0.562548 + 2.58599i) q^{28} +(0.566767 - 0.491106i) q^{29} +(0.122055 - 6.20322i) q^{30} +(8.10734 + 2.38053i) q^{31} +(0.977147 + 0.212565i) q^{32} +(-3.05382 + 2.28606i) q^{33} +(-0.718617 + 1.57355i) q^{34} +(1.14390 + 5.80608i) q^{35} +(-0.668731 + 4.65113i) q^{36} +(-1.27823 + 5.87592i) q^{37} +(1.88621 + 3.45434i) q^{38} +(16.3639 - 2.35277i) q^{39} +(2.17519 + 0.518202i) q^{40} +(-7.72122 - 4.96213i) q^{41} +(-0.523855 - 7.32445i) q^{42} +(9.52665 + 5.20194i) q^{43} +(-0.571117 - 1.25057i) q^{44} +(-1.69963 + 10.3688i) q^{45} +(-3.75982 + 2.97721i) q^{46} +(-2.78897 - 2.78897i) q^{47} +(-2.59975 - 0.969658i) q^{48} +(0.00107183 + 0.00365032i) q^{49} +(4.84014 + 1.25419i) q^{50} +(2.59502 - 4.03793i) q^{51} +(-0.425051 + 5.94299i) q^{52} +(0.821926 - 1.09796i) q^{53} +(1.32811 - 4.52314i) q^{54} +(-1.22180 - 2.82095i) q^{55} +(2.61953 + 0.376632i) q^{56} +(-3.81634 - 10.2320i) q^{57} +(-0.262077 - 0.702656i) q^{58} +(-8.33749 - 1.19875i) q^{59} +(-5.76945 - 2.28216i) q^{60} +(0.141177 - 0.480803i) q^{61} +(5.06366 - 6.76426i) q^{62} +(-0.887149 + 12.4040i) q^{63} +(0.540641 - 0.841254i) q^{64} +(-1.21168 + 13.2677i) q^{65} +(1.07472 + 3.66017i) q^{66} +(3.10707 + 1.15888i) q^{67} +(1.22321 + 1.22321i) q^{68} +(11.5018 - 6.69210i) q^{69} +(5.83975 + 0.957241i) q^{70} +(-5.61249 - 12.2896i) q^{71} +(4.12417 + 2.25197i) q^{72} +(-1.04366 - 14.5923i) q^{73} +(5.05875 + 3.25106i) q^{74} +(-12.7980 - 5.35587i) q^{75} +(3.89570 - 0.560117i) q^{76} +(-1.74370 - 3.19335i) q^{77} +(3.51416 - 16.1543i) q^{78} +(0.692476 - 4.81627i) q^{79} +(1.24568 - 1.85695i) q^{80} +(0.422345 - 0.924807i) q^{81} +(-7.34755 + 5.50031i) q^{82} +(-0.232287 - 0.0505310i) q^{83} +(-7.04571 - 2.06881i) q^{84} +(2.68084 + 2.78846i) q^{85} +(8.20318 - 7.10810i) q^{86} +(0.442318 + 2.03330i) q^{87} +(-1.37131 + 0.0980779i) q^{88} +(11.7514 - 3.45054i) q^{89} +(9.12109 + 5.21600i) q^{90} +15.7681i q^{91} +(1.47558 + 4.56319i) q^{92} +(-16.5782 + 16.5782i) q^{93} +(-3.58776 + 1.63848i) q^{94} +(8.73401 - 1.08085i) q^{95} +(-1.81704 + 2.09698i) q^{96} +(-6.07227 + 1.32094i) q^{97} +(0.00379474 + 0.000271405i) q^{98} +(-0.919379 - 6.39442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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